utf8

11institutetext:  PRHLT Research Center, Universitat Politècnica de València,
Spain
11email: {bigha@doctor, <EMAIL_ADDRESS>22institutetext: AUSY R&D, Paris,
France
22email<EMAIL_ADDRESS>33institutetext: IRIT, CNRS, Université de Toulouse,
France
33email<EMAIL_ADDRESS>
# Irony Detection in a Multilingual Context

Bilal Ghanem 11 Jihen Karoui 22 Farah Benamara 33 Paolo Rosso 11 Véronique
Moriceau 33

###### Abstract

This paper proposes the first multilingual (French, English and Arabic) and
multicultural (Indo-European languages vs. less culturally close languages)
irony detection system. We employ both feature-based models and neural
architectures using monolingual word representation. We compare the
performance of these systems with state-of-the-art systems to identify their
capabilities. We show that these monolingual models trained separately on
different languages using multilingual word representation or text-based
features can open the door to irony detection in languages that lack of
annotated data for irony.

###### Keywords:

Irony Detection Social Media Multilingual Embeddings

##  1 Motivations

Figurative language makes use of figures of speech to convey non-literal
meaning [16, 2]. It encompasses a variety of phenomena, including metaphor,
humor, and irony. We focus here on irony and uses it as an umbrella term that
covers satire, parody and sarcasm.

Irony detection (ID) has gained relevance recently, due to its importance to
extract information from texts. For example, to go beyond the literal matches
of user queries, Veale enriched information retrieval with new operators to
enable the non-literal retrieval of creative expressions [40]. Also, the
performances of sentiment analysis systems drastically decrease when applied
to ironic texts [5, 19]. Most related work concern English [17, 21] with some
efforts in French [23], Portuguese [7], Italian [14], Dutch [26], Hindi [37],
Spanish variants [31] and Arabic [22, 11]. Bilingual ID with one model per
language has also been explored, like English-Czech [32] and English-Chinese
[38], but not within a cross-lingual perspective.

In social media, such as Twitter, specific hashtags (#irony, #sarcasm) are
often used as gold labels to detect irony in a supervised learning setting.
Although recent studies pointed out the issue of false-alarm hashtags in self-
labeled data [20], ID via hashtag filtering provides researchers positive
examples with high precision. On the other hand, systems are not able to
detect irony in languages where such filtering is not always possible.
Multilingual prediction (either relying on machine translation or multilingual
embedding methods) is a common solution to tackle under-resourced languages
[6, 33]. While multilinguality has been widely investigated in information
retrieval [27, 34] and several NLP tasks (e.g., sentiment analysis [3, 4] and
named entity recognition [30]), no one explored it for irony.

We aim here to bridge the gap by tackling ID in tweets from both multilingual
(French, English and Arabic) and multicultural perspectives (Indo-European
languages whose speakers share quite the same cultural background vs. less
culturally close languages). Our approach does not rely either on machine
translation or parallel corpora (which are not always available), but rather
builds on previous corpus-based studies that show that irony is a universal
phenomenon and many languages share similar irony devices. For example, Karoui
et. al [24] concluded that their multi-layer annotated schema, initially used
to annotate French tweets, is portable to English and Italian, observing
relatively the same tendencies in terms of irony categories and markers.
Similarly, Chakhachiro [8] studies irony in English and Arabic, and shows that
both languages share several similarities in the rhetorical (e.g.,
overstatement), grammatical (e.g., redundancy) and lexical (e.g., synonymy)
usage of irony devices. The next step now is to show to what extent these
observations are still valid from a computational point of view. Our
contributions are:

  1. I.

A new freely available corpus of Arabic tweets manually annotated for irony
detection111The corpus is available at
https://github.com/bilalghanem/multilingual˙irony.

  2. II.

Monolingual ID: We propose both feature-based models (relying on language-
dependent and language-independent features) and neural models to measure to
what extent ID is language dependent.

  3. III.

Cross-lingual ID: We experiment using cross-lingual word representation by
training on one language and testing on another one to measure how the
proposed models are culture-dependent. Our results are encouraging and open
the door to ID in languages that lack of annotated data for irony.

##  2 Data

Arabic dataset (Ar=$11,225$ tweets). Our starting point was the corpus built
by [22] that we extended to different political issues and events related to
the Middle East and Maghreb that hold during the years $2011$ to $2018$.
Tweets were collected using a set of predefined keywords (which targeted
specific political figures or events) and containing or not Arabic ironic
hashtags (سخرية¿#, مسخرة¿#, تهكم¿#, استهزاء¿#) 222All of these words are
synonyms where they mean ”Irony”.. The collection process resulted in a set of
$6,809$ ironic tweets ($I$) vs. $15,509$ non ironic ($NI$) written using
standard (formal) and different Arabic language varieties: Egypt, Gulf,
Levantine, and Maghrebi dialects.

To investigate the validity of using the original tweets labels, a sample of
$3,000$ $I$ and $3,000$ $NI$ was manually annotated by two Arabic native
speakers which resulted in $2,636$ $I$ vs. $2,876$ $NI$. The inter-annotator
agreement using Cohen’s Kappa was $0.76$, while the agreement score between
the annotators’ labels and the original labels was $0.6$. Agreements being
relatively good knowing the difficulty of the task, we sampled $5,713$
instances from the original unlabeled dataset to our manually labeled part.
The added tweets have been manually checked to remove duplicates, very short
tweets and tweets that depend on external links, images or videos to
understand their meaning.

French dataset (Fr=$7,307$ tweets). We rely on the corpus used for the DEFT
2017 French shared task on irony [5] which consists of tweets relative to a
set of topics discussed in the media between 2014 and 2016 and contains topic
keywords and/or French irony hashtags (#ironie, #sarcasme). Tweets have been
annotated by three annotators (after removing the original labels) with a
reported Cohen’s Kappa of $0.69$.

English dataset (En=$11,225$ tweets). We use the corpus built by [32] which
consists of $100,000$ tweets collected using the hashtag #sarcasm. It was used
as benchmark in several works [13, 18]. We sliced a subset of approximately
$11,200$ tweets to match the sizes of the other languages’ datasets.

Table 1 shows the tweet distribution in all corpora. Across the three
languages, we keep a similar number of instances for train and test sets to
have fair cross-lingual experiments as well (see Section 4). Also, for French,
we use the original dataset without any modification, keeping the same number
of records for train and test to better compare with state-of-the-art results.
For the classes distribution (ironic vs. non ironic), we do not choose a
specific ratio but we use the resulted distribution from the random shuffling
process.

Table 1: Tweet distribution in all corpora. | # Ironic | # Not-Ironic | Train | Test
---|---|---|---|---
Ar | $6,005$ | $5,220$ | $10,219$ | $1,006$
Fr | $2,425$ | $4,882$ | $5,843$ | $1,464$
En | $5,602$ | $5,623$ | $10,219$ | $1,006$

##  3 Monolingual Irony Detection

It is important to note that our aim is not to outperform state-of-the-art
models in monolingual ID but to investigate which of the monolingual
architectures (neural or feature-based) can achieve comparable results with
existing systems. The result can show which kind of features works better in
the monolingual settings and can be employed to detect irony in a multilingual
setting. In addition, it can show us to what extend ID is language dependent
by comparing their results to multilingual results. Two models have been
built, as explained below. Prior to learning, basic preprocessing steps were
performed for each language (e.g., removing foreign characters, ironic
hashtags, mentions, and URLs).

Feature-based models. We used state-of-the-art features that have shown to be
useful in ID: some of them are language-independent (e.g., punctuation marks,
positive and negative emoticons, quotations, personal pronouns, tweet’s
length, named entities) while others are language-dependent relying on
dedicated lexicons (e.g., negation, opinion lexicons, opposition words).
Several classical machine learning classifiers were tested with several
feature combinations, among them Random Forest (RF) achieved the best result
with all features.

Neural model with monolingual embeddings. We used Convolutional Neural Network
(CNN) network whose structure is similar to the one proposed by [25]. For the
embeddings, we relied on $AraVec$ [36] for Arabic, FastText [15] for French,
and Word2vec Google News [29] for English 333Other available pretrained
embeddings models have also been tested. . For the three languages, the size
of the embeddings is $300$ and the embeddings were fine-tuned during the
training process. The CNN network was tuned with 20% of the training corpus
using the $Hyperopt$444https://github.com/hyperopt/hyperopt library.

Results. Table 2 shows the results obtained when using train-test
configurations for each language. For English, our results, in terms of macro
F-score ($F$), were not comparable to those of [32, 39], as we used 11% of the
original dataset. For French, our scores are in line with those reported in
state of the art (cf. best system in the irony shared task achieved $F=78.3$
[5]). They outperform those obtained for Arabic ($A=71.7$) [22] and are
comparable to those recently reported in the irony detection shared task in
Arabic tweets [11, 12] ($F=84.4$). Overall, the results show that semantic-
based information captured by the embedding space are more productive
comparing to standard surface and lexicon-based features.

Table 2: Results of the monolingual experiments (in percentage) in terms of accuracy (A), precision (P), recall (R), and macro F-score (F). Arabic | French | English
---|---|---
| A | P | R | F | A | P | R | F | A | P | R | F
RF | 68.0 | 67.0 | 82.0 | 68.0 | 68.5 | 71.7 | 87.3 | 61.0 | 61.2 | 60.0 | 70.0 | 61.0
CNN | 80.5 | 79.1 | 84.9 | 80.4 | 77.6 | 68.2 | 59.6 | 73.5 | 77.9 | 74.6 | 84.7 | 77.8

##  4 Cross-lingual Irony Detection

We use the previous CNN architecture with bilingual embedding and the RF model
with surface features (e.g., use of personal pronoun, presence of
interjections, emoticon or specific punctuation)555To avoid language
dependencies, we rely on surface features only discarding those that require
external semantic resources or morpho-syntactic parsing. to verify which pair
of the three languages: (a) has similar ironic pragmatic devices, and (b) uses
similar text-based pattern in the narrative of the ironic tweets. As
continuous word embedding spaces exhibit similar structures across (even
distant) languages [28], we use a multilingual word representation which aims
to learn a linear mapping from a source to a target embedding space. Many
methods have been proposed to learn this mapping such as parallel data
supervision and bilingual dictionaries [28] or unsupervised methods relying on
monolingual corpora [10, 1, 41]. For our experiments, we use Conneau et al ’s
approach as it showed superior results with respect to the literature [10]. We
perform several experiments by training on one language ($lang_{1}$) and
testing on another one ($lang_{2}$) (henceforth $lang_{1}\rightarrow
lang_{2}$). We get 6 configurations, plus two others to evaluate how irony
devices are expressed cross-culturally, i.e. in European vs. non European
languages. In each experiment, we took 20% from the training to validate the
model before the testing process. Table 3 presents the results.

Table 3: Results of the cross-lingual experiments.  | CNN | RF
---|---|---
Train$\rightarrow$Test | A | P | R | F | A | P | R | F
Ar$\rightarrow$Fr | 60.1 | 37.2 | 26.6 | 51.7 | 47.03 | 29.9 | 43.9 | 46.0
Fr$\rightarrow$Ar | 57.8 | 62.9 | 45.7 | 57.3 | 51.11 | 61.1 | 24.0 | 54.0
Ar$\rightarrow$En | 48.5 | 26.5 | 17.9 | 34.1 | 49.67 | 49.7 | 66.2 | 50.0
En$\rightarrow$Ar | 56.7 | 57.7 | 62.3 | 56.4 | 52.5 | 58.6 | 38.5 | 53.0
Fr$\rightarrow$En | 53.0 | 67.9 | 11.0 | 42.9 | 52.38 | 52.0 | 63.6 | 52.0
En$\rightarrow$Fr | 56.7 | 33.5 | 29.5 | 50.0 | 56.44 | 74.6 | 52.7 | 58.0
(En/Fr)$\rightarrow$Ar | 62.4 | 66.1 | 56.8 | 62.4 | 55.08 | 56.7 | 68.5 | 62.0
Ar$\rightarrow$(En/Fr) | 56.3 | 33.9 | 09.5 | 42.7 | 59.84 | 60.0 | 98.7 | 74.6

From a semantic perspective, despite the language and cultural differences
between Arabic and French languages, CNN results show a high performance
comparing to the other languages pairs when we train on each of these two
languages and test on the other one. Similarly, for the French and English
pair, but when we train on French they are quite lower. We have a similar case
when we train on Arabic and test on English. We can justify that by, the
language presentation of the Arabic and French tweets are quite informal and
have many dialect words that may not exist in the pretrained embeddings we
used comparing to the English ones (lower embeddings coverage ratio), which
become harder for the CNN to learn a clear semantic pattern. Another point is
the presence of Arabic dialects, where some dialect words may not exist in the
multilingual pretrained embedding model that we used. On the other hand, from
the text-based perspective, the results show that the text-based features can
help in the case when the semantic aspect shows weak detection; this is the
case for the $Ar\longrightarrow En$ configuration. It is worthy to mention
that the highest result we get in this experiment is from the
En$\rightarrow$Fr pair, as both languages use Latin characters. Finally, when
investigating the relatedness between European vs. non European languages (cf.
(En/Fr)$\rightarrow$Ar), we obtain similar results than those obtained in the
monolingual experiment (macro F-score 62.4 vs. 68.0) and best results are
achieved by Ar $\rightarrow$(En/Fr). This shows that there are pragmatic
devices in common between both sides and, in a similar way, similar text-based
patterns in the narrative way of the ironic tweets.

##  5 Discussions and Conclusion

This paper proposes the first multilingual ID in tweets. We show that simple
monolingual architectures (either neural or feature-based) trained separately
on each language can be successfully used in a multilingual setting providing
a cross-lingual word representation or basic surface features. Our monolingual
results are comparable to state of the art for the three languages. The CNN
architecture trained on cross-lingual word representation shows that irony has
a certain similarity between the languages we targeted despite the cultural
differences which confirm that irony is a universal phenomena, as already
shown in previous linguistic studies [35, 24, 9]. The manual analysis of the
common misclassified tweets across the languages in the multilingual setup,
shows that classification errors are due to three main factors. (1) First, the
absence of context where writers did not provide sufficient information to
capture the ironic sense even in the monolingual setting, as in نبدا تاني يسقط
يسقط حسني مبارك !! ¿ (Let’s start again, get off get off Mubarak!!) where the
writer mocks the Egyptian revolution, as the actual president ”Sisi” is viewed
as Mubarak’s fellows. (2) Second, the presence of out of vocabulary (OOV)
terms because of the weak coverage of the mutlilingual embeddings which make
the system fails to generalize when the OOV set of unseen words is large
during the training process. We found tweets in all the three languages
written in a very informal way, where some characters of the words were
deleted, duplicated or written phonetically (e.g phat instead of fat). (3)
Another important issue is the difficulty to deal with the Arabic language.
Arabic tweets are often characterized by non-diacritised texts, a large
variations of unstandardized dialectal Arabic (recall that our dataset has 4
main varieties, namely Egypt, Gulf, Levantine, and Maghrebi), presence of
transliterated words (e.g. the word table becomes طابلة¿ (tabla)), and finally
linguistic code switching between Modern Standard Arabic and several dialects,
and between Arabic and other languages like English and French. We found some
tweets contain only words from one of the varieties and most of these words do
not exist in the Arabic embeddings model. For example in مبارك بقاله كام يوم
مامتش .. هو عيان ولاه ايه #مصر ¿ (Since many days Mubarak didn’t die .. is he
sick or what? #Egypt), only the words يوم¿ (day), مبارك¿ (Mubarak), and هو¿
(he) exist in the embeddings. Clearly, considering only these three available
words, we are not able to understand the context or the ironic meaning of the
tweet.

To conclude, our multilingual experiments confirmed that the door is open
towards multilingual approaches for ID. Furthermore, our results showed that
ID can be applied to languages that lack of annotated data. Our next step is
to experiment with other languages such as Hindi and Italian.

## Acknowledgment

The work of Paolo Rosso was partially funded by the Spanish MICINN under the
research project MISMIS-FAKEnHATE (PGC2018-096212-B-C31).

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# Formation and Study of a Spherical Plasma Liner for Plasma-Jet-Driven
Magneto-Inertial Fusion

A. L. LaJoie  University of New Mexico  F. Chu  Los Alamos National Laboratory
A. Brown  Los Alamos National Laboratory  S. Langendorf  Los Alamos National
Laboratory  J. P. Dunn  Los Alamos National Laboratory  G. A. Wurden  Los
Alamos National Laboratory  F. D. Witherspoon  HyperJet Fusion Corp.  A. Case
HyperJet Fusion Corp.  M. Luna  HyperJet Fusion Corp.  J. Cassibry  University
of Alabama at Huntsville  A. Vyas  University of Alabama at Huntsville  M.
Gilmore  University of New Mexico

###### Abstract

Plasma-jet-driven magneto-inertial fusion (PJMIF) is an alternative approach
to controlled nuclear fusion which aims to utilize a line-replaceable dense
plasma liner as a repetitive spherical compression driver. In this experiment,
first measurements of the formation of a spherical Argon plasma liner formed
from 36 discrete pulsed plasma jets are obtained on the Plasma Liner
Experiment (PLX). Properties including liner uniformity and morphology, plasma
density, temperature, and ram pressure are assessed as a function of time
throughout the implosion process and indicate an apparent transition from
initial kinetic inter-jet interpenetration to collisional regime near
stagnation times, in accordance with theoretical expectation. A lack of
primary shock structures between adjacent jets during flight implies that
arbitrarily smooth liners may be formed by way of corresponding improvements
in jet parameters and control. The measurements facilitate the benchmarking of
computational models and understanding the scaling of plasma liners towards
fusion-relevant energy density.

##  I Introduction

Magneto-inertial fusion (MIF, also called magnetized target fusion or MTF) is
an approach to controlled nuclear fusion which joins aspects of both magnetic
confinement fusion and inertial confinement fusion methods, enabling
controlled fusion at more modest values of both confinement time and density
[1, 2, 3, 4, 5] than those in the purely inertial or magnetic confinement
counterparts. Many MIF compression approaches and configurations have been
proposed and studied, including the Magnetized Liner Inertial Fusion (MagLIF)
Z-pinch configuration [6], shear-flow-stabilized Z pinches [7], spherical
piston-driven liquid metal liners [8], rotationally stabilized liquid metal
liners[9], and staged-gas-puff Z-pinches[10]. Notably, MagLIF experiments have
successfully produced thermonuclear conditions and significant neutron yields
from the compression of preheated magnetized deuterium fuel, on implosion
timescales significantly longer than can be tolerated in pure inertial fusion.

The plasma-jet-driven magneto-inertial fusion (PJMIF) concept is an MIF
approach in which the requisite heavy compressive liner is formed from the
merging and spherical convergence of an array of discrete plasma jets. PJMIF
aims to access an attractive subsection of the MIF physics parameters space,
namely that of the spherical, moderate velocity (50-150 km/s) compression of
high-beta high-Hall-parameter targets which have shown promise in MagLIF [11,
12, 5]. If successful, this architecture would enable repetitive line-
replaceable operation with a significant standoff distance between the fusion
plasma and driver hardware. Achieving economical repetitive operation is a
significant challenge facing all proposed pulsed fusion concepts, in
particular those seeking to utilize electrical pulsed-power as the primary
energy source [4, 11].

There remain several key questions regarding the viability of the PJMIF
approach, including whether conditions of sufficient energy density and fusion
gain can be attained while maintaining the physical standoff that constitutes
a key appeal of the approach, whether sufficient uniformity of a spherical
liner can be attained from the merger of discrete jets in the face of jet-on-
jet shock waves and Rayleigh-Taylor instabilities [13, 14, 15], and whether
effective magnetic insulation of a standoff target plasma can be achieved in
spherical implosion geometry [16]. Prior investigations have shed light on
several of these questions, with analytical and computational modeling
predicting the feasibility of significant fusion gain [17], the realization of
high-performance modular plasma guns to produce controlled plasma jets [18],
and laboratory experiments studying the merging and formation processes of
multiple plasma jets at representative velocities [19, 20, 21, 22, 23]. Much
of the experimental work has been done at the Plasma Liner Experiment (PLX) at
Los Alamos, a moderate-scale experimental effort towards understanding the
challenges and scaling of PJMIF. Early experimental campaigns at PLX focused
on plasma gun development and generating suitable pulsed-power-driven jets
[18, 24], while more recent campaigns have been aimed at understanding and
characterizing jet merging behavior in obliquely merging jet pairs [19, 20],
and liner subsection formation of up to 6 or 7 jets [4, 21].

In the present work, fully spherical plasma liners have been formed and
investigated at the Plasma Liner Experiment (PLX). This experiment uses 36
individual argon plasma jets, enabling observation of the integrated liner
assembly process for the first time. The primary aim is to assess the
uniformity and plasma characteristics of the full spherical liner formed by
discrete jets and determine where future work must focus to close the gap
between present liner quality and fusion-relevant characteristics. The
discussion of this full liner experimental campaign is organized as follows:
Section II details the pulsed power setup and plasma jet formation and tuning,
Section III describes what plasma properties are measured and the diagnostics
used to do so, and Section IV presents the results of the diagnostic suite and
implications for PJMIF as a whole. Considerations necessary for continuation
and an eventual reactor-scale device are explored in Section VI as well as a
concluding summary of points.

##  II Experiment

Figure 1:  Photo of the PLX chamber alongside a rendering of the fully
assembled plasma liner and target. The present study focuses exclusively on
the plasma liner behavior.

The PLX device consists of a 3-meter diameter chamber and 36 attached plasma
guns, shown in Fig. 1 along with a rendered cross section of the chamber and
notional plasma liner and target within [12]. The plasma guns are positioned
quasi-spherically over the chamber, with an average full-angle between
adjacent guns of 36 degrees and a minimum full-angle of 22 degrees due to the
relative positioning of available gun attachment ports. Chamber vacuum base
pressure is typically around 1 $\mu$torr before plasma jets are injected into
the chamber, increasing to $\sim$ 10 $\mu$torr when a turbopump gate valve is
closed before the shot.

The plasma guns that supply the liner-forming plasma jets are contoured-gap
coaxial plasma railguns - the contoured shape of the inner electrode
alleviates the blowby instability in such geometries that can hinder outgoing
jet quality. The guns used in the present PLX work are similar to those
described in detail in Ref[18], although the current PLX ones are a more
compact design. The stored energy per gun per pulse is 4.5-6 kJ, which
accelerates argon plasma jets of total mass $\sim$1 mg to typical tunable
velocities between 30 and 70 km/s out of a barrel that is 8.5 cm in diameter.
Most of the plasma gun capacitor banks and spark-gap switches are mounted
directly onto the chamber to minimize transfer inductance to the plasma load
and increase energy coupling. Due to space access limitations around the
lowest ports of the PLX chamber, nine guns are instead linked to their
capacitor banks via an array of transmission lines, referred to hereafter as
transmission line (TL) guns. Plasma properties of the jets at the time of
ejection have been explored in previous publications [20]; typically, for a
given jet around ejection time, $T_{e}\approx 1.5-2.0$ eV and $n_{e}\approx
10^{16}$ cm-3.

Four distinct collections of capacitor banks are activated when firing a PLX
shot. The first is a high voltage (19.0 kV) modified-Blumlein trigger network
for the plasma gun gas valves. This sends 36 trigger pulses down coaxial
cables to 36 spark gap switches that operate the gas valve capacitor banks of
the plasma guns. Each plasma gun has a separate 100 J capacitor bank that
actuates the gun’s fast gas puff valve, injecting neutral argon gas injection
into the guns. An adjustable time delay passes while gas valves operate and
neutral gas flows into the bore of the plasma guns, typically 480 microseconds
in the current experiments. Thirdly, another modified-Blumlein trigger network
fires, to breakdown the parallel spark-gaps for the main gun banks. These
banks have 575 $\mu$F rated to 5 kV peak voltage, and provide most of the
current to form and accelerate the plasma jet. The main bank is discharged
across a set of six spark-gap switches to the coaxial rail electrodes, again
to minimize transfer inductance and prolong switch electrode lifetime.
Operating voltages are set to 4.0 kV for non-TL guns, while the TL guns
described above are charged to 4.5 kV to compensate for the increased transfer
inductance of their transmission lines. Time $t=0$ is defined as when the main
trigger pulse for the main accelerating banks is sent. Pressure adjustments
can be made to many of the spark-gap switches on a per-gun basis to ensure
they all break down properly with the trigger pulse. A resistive circuit in
parallel with the pulse-forming-network (PFN) spark-gap trigger switches
produces pre-ionization at the breech - this preionization reduces time jitter
of the bulk plasma breakdown and subsequent acceleration generated by the main
bank.

Tuning the individual jet velocity is essential in this experiment, in order
to ensure the jets arrive in the chamber at the same time and merge together
with as high degree of spherical symmetry as possible. The component voltages
described above can be adjusted for varying effects: a higher main trigger
voltage can reduce firing jitter but increases probability of prefiring and
arcing between components; main bank charge voltage establishes the overall
energy with which the jets are ionized and accelerated; GV charge voltages
establish how much gas is injected into the breach and subsequently
accelerated. The most robust means of tuning jet velocity is adjusting the GV
bank voltage and therefore the injected mass into which the accelerating PFN
energy is deposited. To achieve a nominal jet front velocity $v_{j}$ of 50
km/s for each of the 36 jets, adjustments to this GV bank voltage for each
individual gun are made approximately 2 seconds to firing to fine-tune the
respective jet velocity. This tuning method enables significantly more
flexible and easier adjustment than the previous method of introducing ballast
impedence wires in series with the GV described in Appendix B of Ref[21].
Results in this paper are obtained using a nominal best tune of each gun to 50
km/s. The process of determining the best tune is described in Section III.2.
Mach number $M=v_{jet}/c_{s}$, with $c_{s}=[\gamma
p/\rho]^{1/2}=[\gamma/m_{i}(\bar{Z}T_{e}+T_{i})]^{1/2}$, where adiabatic index
$\gamma=5/3$ is assumed and $m_{i}$ is the Argon ion mass. To estimate $M$, we
will use calculations from previous work examining the exiting jet for
temperature $T_{e}=T_{i}\approx 1.5$ and $\bar{Z}\approx 1.0$. With these
values, estimated ejection Mach number in the present experiment is around
$M\approx 14$.

Main bank and GV discharges are monitored using a set of Rogowski coils on
each gun: six on the main bank transmission lines and one on the GV
transmission line. Signals from these are sent to a static integrator box to
convert the measured $dI/dt$ to $I(t)$ where $I$ is current. It has been
empirically determined that jet ejection time corresponds to about 2.5 $\mu$s
after the peak of the main bank Rogowski current signal. Figure 2 shows a set
of all 36 main bank Rogowski signals, the mean signal and standard deviation
zone around it, and the mean ejection time given by the dashed line. Current
ringing is observed after the primary accelerating current corresponding to
the signal peak, as the underdamped capacitor circuit discharges its remaining
energy into residual trailing plasma in the gun.

Figure 2:  Rogowski coil signals for all 36 guns on a shot. Mean signal and
standard deviation zone are shown as black curve and grey band. The dashed
line is the mean ejection time of all jets. The inset shows a zoomed in
portion around the jet ejection time.

##  III Diagnostics

A suite of diagnostics is used to interrogate the plasma liner properties
throughout the merge and stagnation process. Time-resolved laser
interferometry measurements of line-integrated plasma density are acquired
over the duration of each shot, and a multi-frame fast camera images the
plasma at several times throughout each shot. A collection of single-frame
wide-view cameras are also used for imaging. Photodiode time-of-flight pairs
are used measure individual jet velocities for each of the 36 plasma jets.
Individual gun performance is also monitored using Rogowski coils that measure
the main accelerating current of each gun (see Fig. 2). An imaging
spectrometer provides electron temperature and charge state information and
high-resolution spectrometer is used to verify electron density and jet
slowing at chamber center. Diagnostics lacking inherent time-resolution are
instead triggered at varying times for different shots to build up an average
picture of temporal evolution of the liner. Figure 3 indicates generally the
layout and viewing arrangements of most of the diagnostics in the experimental
campaign (the wide-view cameras are not indicated, as each has a view of the
entire chamber interior).

Figure 3:  Diagram of PLX and most of the central sight lines, indicated as
dash-dotted lines, of the primary diagnostics. Spatial separations, angles,
and placements are not necessarily to scale, and for ease of visualization,
all diagnostics are shown here to be in the same 2D plane which is not the
case on the actual 3D chamber.

###  III.1 Imaging

A multi-frame intensified Hadland UHSi24 camera in 12-frame mode and outfitted
with a 24 mm focal length lens at f-number 11, provides a focused view of the
chamber center where the ultimate liner stagnation occurs. A typical exposure
time per frame of 25 ns is used with adjustable framerate set to 200 kHz.
Additionally, a set of four single-frame PCO Pixelfly-USB cameras each
outfitted with a 2.7 mm focal length fisheye lens at f-number 16 provide 1
$\mu$s exposure wide-angle images of the entire chamber and liner assembly and
convergence process. These are set into the chamber via re-entrant ports
described in detail in Ref[25] so as to provide each with a view of the entire
chamber interior. These Pixelfly cameras originally were intended to be used
together (as a set of 6) to determine jet velocities of all 36 jets within a
single shot [25], but the photodiode method described in the next subsection
proved to be a more reliable method for jet velocimetry.

Figure 4:  Diagram illustrating photodiode time-of-flight pair operation. The
two diagrams represent the times $t_{1}$ and $t_{2}$, each indicated on a
typical photodiode pair signal after smoothing. The velocity indicated is
obtained via signal cross correlation within the highlighted region.

###  III.2 Photodiode Pairs

Each gun is equipped with two light-collecting fibers positioned along the jet
trajectory and spaced by 2 cm which feed to two photodiodes having
sufficiently fast risetime to track the jet (5 ns). The collection fibers are
recessed into their holders by 6 mm to limit the light collection cone. The 2
cm separation distance was selected as a compromise between two competing
considerations: there must be enough time separation between the signals that
the available digitization rate of 40 MHz does not significantly contribute to
uncertainty (i.e. there are sufficient samples separating the two signals),
and the closer together the fibers are the signals are more likely to be
closely correlated in shape which enables easier analysis.

Figure 4 shows a diagram of the two photodiode views of a jet, at two times of
jet emergence from the gun cavity. The corresponding locations on normalized
sample signal readouts are also indicated, along with the region within which
a cross correlation is applied. The bounds of the cross correlation region are
selected to be a few microseconds before the signal rises, and a few
microseconds after the signal peak. This provides the jet front velocity. The
jets consist of a distribution of directed velocities with the trailing
portion being slower than the jet front, resulting in an extended column of
plasma. The velocity analysis focuses on the front region because this the
portion which forms the spherical liner to compress the MIF target and is
therefore most relevant. The photodiode analysis process is automated and
repeated for each gun and enables velocities to be measured immediately
following each shot and tuned as desired by adjusting the GV bank voltage -
this we call the tuned velocity setting.

Figure 5:  Comparison of jet velocity determined from a single-tip Langmuir
probe and from the photodiode methodology described in Section III.2. The
first column shows a) the Rogowski coil signal with jet ejection time and b)
chamber-center probe signal with first-peak feature representing jet arrival
time to probe. The second column indicates c) photodiode signals and d) cross
correlation of those signals used to determine velocity.

This photodiode pair time-of-flight velocimetry methodology was cross-checked
by taking a set of shots with a single gun at a time while positioning a
single-tip Langmuir probe at chamber center, and obtaining a jet velocity via
the plasma time-of-flight to the probe ($V_{prb}$) and comparing to the
velocity inferred via the photodiode signals ($V_{PD}$). A typical comparison
is shown in Fig. 5. In this, we define the jet arrival time to the probe as
the location corresponding to 20% of the full integral of the probe signal.
The previously discussed jet ejection time is subtracted from this arrival
time, and in conjunction with the travel distance being the PLX radius of
136.5 cm, provides $V_{prb}$. This generally matches well with the first peak-
like feature in the signal, as seen in subfigure b.

It was found that even with a careful analysis methodology, the photodiode
velocimetry incurred additional shot-to-shot variation in inferred velocity
compared to the probe time-of-flight technique. This is believed to be due to
early time spatial structure and inhomogeneity in the plasma jet. A tune
setting was selected for final use if the mean velocity measured on the
photodiodes was 50 $\pm$ 10 km/s over about 5 shots.

###  III.3 High Resolution Spectroscopy

Single-emission-line shapes are acquired using a 2 m double-pass (for a 4 m
focal length) high-resolution monochromator (McPherson 2062DP) with 2400 mm-1
grating and 50 $\mu$m slit width, with the resulting spectrum captured with a
1 $\mu$s exposure on a PCO Pixelfly camera. The emission studied in this work
is the Ar II 480.60 nm line due to its relatively high intensity among the
other visible band Ar II emission lines, in addition to a lack of local lines
from higher ionization states or impurities. The line of sight (LOS) of this
spectrometer is directly through PLX chamber center.

For this plasma emission line profile, there are three primary plasma factors
that we find to impact the observed shape. Bulk motion of the plasma
throughout the LOS causes Doppler shift of the observed emission wavelength,
and a distribution of bulk plasma motion results in a corresponding
distribution of shifts. Doppler broadening associated with the plasma
temperature of this distribution is also present. Finally, Stark broadening
associated with the electron density in the vicinity of emitters also impact
the observed shape.

At the stagnation densities of $\sim 10^{17}$ cm-3, the time required for
equilibration of electron and ion temperatures is far shorter than the
$\sim\mu$s timescales over which the plasma evolves. We assess this using the
Coulomb collision expression for temperature equilibration given in Eq. 1 in
which species $\alpha$ corresponds to ions and $\beta$ to electrons, and
$\bar{\nu}_{\epsilon}^{\alpha\backslash\beta}$ is the energy-exchange
frequency in units of s-1 between electrons and ions given in Eq. 2:

$\frac{dT_{\alpha}}{dt}=\bar{\nu}_{\epsilon}^{\alpha\backslash\beta}(T_{\beta}-T_{\alpha})$
(1)

$\bar{\nu}_{\epsilon}^{\alpha\backslash\beta}=$1.8\text{\times}{10}^{-19}$\frac{(m_{\alpha}m_{\beta})^{1/2}Z_{\alpha}^{2}Z_{\beta}^{2}n_{\beta}\lambda_{\alpha\beta}}{(m_{\alpha}T_{\beta}+m_{\beta}T_{\alpha})^{3/2}}$
(2)

With typical expected conditions of $T_{e}=2.5$ eV,
$n_{e}=$3\text{\times}{10}^{17}$$ cm-3, and supposing ion temperature $T_{i}$
is moderately elevated at $10$ eV, the resulting time required for temperature
equilibration between electrons and ions is on the order of nanoseconds. Thus,
$T_{i}\approx T_{e}=T$ and are also clamped to values around 2.5 eV - as
indicated by broadband emission spectroscopy results in Section IV.3. Thus
ultimately, Doppler broadening is found to be negligible in comparison to the
other two broadening mechanisms, meaning that the high resolution lineshapes
are more useful for density and residual velocity inference than for
temperature determination.

###  III.4 Multi-Chord Interferometry

Line-integrated electron density is obtained in this work via a multi-chord
heterodyne laser interferometry system whose arrangement is laid out in
Ref[26]. The laser emission is produced using a 320 mW, 561 nm solid state
laser, is split into multiple lower-power beams and injected into the chamber
through five single-mode fiber optic cables with each probe beam about 0.3 cm
in diameter. The scene chords of the interferometer are aligned parallel to
one another, with a central chord passing through the center of the chamber,
and the others in pairs, offset from the central by 12.75 cm and 25.5 cm
respectively. Thus the chords measure the coarse radial density profile as
well as provide a check against the spherical symmetry of the liner (if a
perfectly spherical plasma liner is formed, the signals on the chord pairs
should perfectly match). After passing through the plasma, the probe beams are
compared with a reference beam of the interferometer in the Mach-Zender
configuration, and the line-integrated electron density is computed based on
the relative phase shift [27, 26].

###  III.5 Spatially-Resolved Emission Spectroscopy

Spatially-resolved visible plasma emission spectra provides insight into LOS-
integrated behavior of electron temperature via relative line emission
intensities, and relative plasma density via observed Bremsstrahlung emission
intensity. In the Multi-Chord Spectrometer (MCS), data is collected along 11
fiber-coupled lines of sight through 2.5 cm diameter collimating lens of 6 cm
focal length mounted outside the chamber, with waist size of 1 cm. This light
is focused on the entrance slit of a Chromex 500is imaging spectrometer with
0.5 m focal length, a 1200 grooves/mm grating and 50 $\mu$m slit for an
effective resolution of 0.08 nm over the wavelength range used, 453.3 nm to
482.2 nm. A relative intensity calibration was applied based on a calibrated
tungsten Thorlabs SLS201L lamp shining through the same set of windows and
optics as the PLX plasma light traverses. An additional calibration measure
was taken to normalize the total amount of light collected through each fiber;
to do so, each fiber was illuminated individually with the lamp and imaged
with constant camera settings, allowing for comparison of counts vs.
wavelength for all fibers.

A sample spectral image is shown in Fig. 6, as well as a spectrum
corresponding to the highlighted region of fiber 2 after vertical summing of
region signal counts and applying the intensity calibration. This process is
repeated for respective fiber regions to obtain the 11 chordal spectra per
image. The presence or lack of emissions from the Ar ionization stages
constrains the temperature regime to electron temperatures of $\sim$few eV.
More precisely, the best-fit line-integrated electron temperature is inferred
by comparing the observed emission spectrum to a set synthetic spectra of
varying temperature generated by the collisional-radiative spectral analysis
model PrismSPECT. PrismSPECT generates an emission spectrum based on excited
state densities that it calculates via a collisional-radiative model in a non-
local thermodynamic equilibrium regime. The atomic level scheme utilized in
the model includes excited states up to Ar IV, after which only ground states
of ionic stages are considered (and are all of negligible populations).

Figure 6:  a) MCS spectral image obtained with 1 $\mu$s exposure taken 45.4
$\mu$s after jet ejection time, around stagnation. Chord 2 (second-closest to
chamber center) region is highlighted in white. b) Spectrum of chord 2 region,
summed along vertical pixels within the highlighted region.

The measured-to-synthetic spectra comparison is made after having subtracted
off the continuum background from the MCS spectra. The PLX liner sweeps up
residual air in the chamber as it travels inwards, so the observed spectra
contain N and O lines in addition to the Ar lines, though no other
contaminants are observed. The different chords of the MCS observe different
amounts of these N and O lines relative to the Ar lines, so modeled spectra
are generated for different elemental compositions as well. After the entire
set of composite synthetic spectra at varying $T_{e}$ and compositions are
generated, a simple least-squares method is performed to select that which
matches closest to the observed MCS spectrum for a given chord, and we take
that $T_{e}$ as the LOS-integrated representative temperature for that chord.

Another characteristic that the MCS provides is LOS-averaged plasma density
relative to that of the central chord (this doesn’t involve comparison to
PrismSPECT). This is a relative measurement due to lack of absolute intensity
calibration with the spectrometers. Not considering all factors which do not
depend strongly on density, the free-free (Bremsstrahlung) emissivity scales
as:

$\varepsilon_{ff}\propto\sum_{i}n_{e}Z_{i}^{2}n_{i}$ (3)

and the free-bound (radiative recombination) emissivity scales as:

$\varepsilon_{fb}\propto\sum_{i}\frac{n_{e}Z_{i}^{2}n_{i}}{U_{i}}$ (4)

in which $U_{i}$ is its partition function [28, 29].

Our plasma is primarily comprised of Ar+ and Ar2+, so electron density
$n_{e}\approx n_{+}+2n_{2+}$. Given this, the combination of free-free
emission and free-bound radiation scales as $n_{e}^{2}$, so we need only have
a reasonable knowledge of $n_{e}$ and mean charge state
$\bar{Z}\approx\frac{n_{e}}{n_{+}+n_{2+}}$ to have the necessary scaling
relation between continuum intensity to spatially-resolved relative plasma
density. These characteristics are quantified in Section IV.3. A notable
feature discussed in that section is the presence of N and O constituents in
the plasma which add their own contributions to $n_{e}$ and thus complicate
the scaling behavior in $\epsilon_{ff}$ and $\epsilon_{fb}$ \- however, we
will still retain the relation $(\epsilon_{ff}+\epsilon_{fb})\propto
n_{e}^{2}$ as an approximation.

##  IV Results

Figure 7: False color images from a series of different shots at different
times throughout the jet ejection and merge process from one of the fisheye
cameras, with counts shown on a logarithmic scale.

###  IV.1 Imaging

A series of images from the Pixelfly fisheye cameras is shown Fig. 7, and
illustrates the general behavior from jet ejection to initial merge and
finally to central stagnation. The liner assembly begins between 11 and 17
$\mu$s. Stagnation and the brightest moment occurs around 46 $\mu$s. It should
be noted that because each image corresponds to a different shot, jet
velocities may deviate slightly between each image as a result of shot-to-shot
variation (see Fig. 11). In contrast, the set of images shown in Fig. 8 are
from a single shot using the multi-frame Hadland camera. Both the Pixelfly
images and Hadland images indicate a uniform liner is indeed formed by the 36
discrete jets with shockless morphology en route to chamber center, as opposed
to earlier observations using a smaller subset of guns [21, 20] operating at
different conditions. Hadland multi-frame imaging of the process for a single
shot also shows a liner stagnation which maintains good sphericity, deviating
slightly in some frames towards a more oblate shape. This may be related to
the 9 TL guns on the bottom of the chamber which necessarily fire with
slightly different settings than the other guns as discussed in Section II.
The dissipation time that the overall emission strength recedes back to
background levels is around 40 $\mu$s after stagnation.

Figure 8:  Single shot image set from the multi-frame Hadland ICCD camera.
Image times after ejection are included as well as the spatial scale.
Exposures are 25 ns, and image counts are shown on a heatmap with a
logarithmic scale. This shot is the same as that for which Rogowski coil
signals were shown in Fig. 2. Figure 9:  Photodiode signals for several guns
and the resulting velocity from cross correlation within the marked region.
Despite the diversity of signal shapes, velocities are relatively consistent.

###  IV.2 Jet Velocities and Liner Merging

Photodiode signals for several guns are shown in Fig. 9 in which one observes
a diversity of photodiode signal shapes observed. One potential source of the
form variation is that the jets are expelled from the gun with more turbulent
structure than anticipated. This variation in shapes practically means that
certain jets have their velocities determined more reliably than others.

Velocities averaged over a set of 30 shots are shown in Fig. 10. Uncertainties
are more so a result of shot-to-shot variation rather than in the analysis
methodology. This variation is visualized in Fig. 11, in which the three shots
shown give rather different velocity values, which can be qualitatively
confirmed by noting the separation of the two signals in e.g. subplot a.
versus those in b. Although shot-to-shot variation is evident in the magnitude
of the error bars, mean values over the shot series generally fall within
$\pm$ 10 km/s of the targeted 50 km/s with few outliers - the tuning of gun 34
for example was ineffective as the reduction in GV voltage necessary to
elevate its velocity also prevented its firing at all. The velocity
determination method discussed in Section III.2 returns clearly erroneous
velocity values in about 10% of cases (by-hand calculation based on signal
separation in these cases sharply disagrees with those calculated via the
cross correlation method). To discard these as outliers, for a given jet on a
given shot only calculated front velocities between 20 and 85 km/s are
accepted. With present gun settings it is unlikely jets are fired at
velocities truly outside these bounds.

Figure 10:  Mean velocities and standard deviations (error bars) of all 36
guns, averaged over a set of 30 shots over which tune values are unchanged and
selected to nominally obtain 50 km/s jet front speeds for all jets. Figure 11:
Photodiode signals from a single gun for three different shots, with three
different calculated velocities, indicative of shot-to-shot variation.

###  IV.3 Spatially-Resolved Emission Spectroscopy

Table 1: PrismSPECT parameters corresponding to those in Fig. 12.  Model Property | Value (Ar / N / O)
---|---
Overall ion density |  $1.0\text{\times}{10}^{17}$ cm-3
Plasma thickness | 15 cm
Matched electron temperature | 2.5 eV
Matched composition | 0.6 / 0.18 / 0.22
Matched mean ion charge | 1.8 / 1.4 / 1.2

While the combination of shot-to-shot velocity variation and jet-to-jet
variation within a single shot constrains attainable liner uniformity, it
remains sufficiently minimal to provide some interesting results throughout
the merge process by examining a collection of shots. Spectra observed with
the MCS spatially-resolved spectroscopy system indicates a marked rise in
presence of air lines closer to the central chord (chord 1). A sample spectrum
from the central chord of the MCS is shown in Fig. 12, along with synthetic
PrismSPECT spectra generated using the characteristics denoted in Table 1. The
best matching synthetic spectrum of a set with varying properties is the red
curve in subfigure b., corresponding to an electron temperature of 2.5 eV, an
Ar fraction of 0.6, and the remaining composition split nearly equally between
N and O species. That N and O are present in roughly equal quantities instead
of a fraction similar to air suggests that some oxygen is desorbed from
plasma-facing surfaces in the chamber during a shot, elevating it more than
the ordinary air fraction. The fraction of N and O increases for the LOS
closer to chamber center. Mean charge state $\bar{Z}$ is another parameter
determined via this PrismSPECT comparison, with argon $\bar{Z}\approx 1.8\pm
0.14$ for the above conditions.

Performing the comparison to PrismSPECT for all fibers at times throughout
liner formation and implosion provides a number of interesting insights,
summarized in Fig. 13. There is a center-wards (lower fiber number) decrease
in Ar amount, observed in subfigure b. This decrease is not attributable to
changes in electron temperature $T_{e}$ which remains at about 2.5 $\pm$ 0.18
eV over space and time as indicated in subfigure a., and is instead evidence
of the residual chamber air being swept up by the liner front. The unchanging
nature of $T_{e}$ was also observed in an earlier PLX study involving merging
of only a few guns [21]. Another striking feature of the spectra is evolution
of continuum emission intensity from increasing Bremsstrahlung and bound-free
emissions illustrated in subfigure c. This provides relative plasma density
behavior spatially and temporally, as the continuum intensity scales as
$n_{e}^{2}$, as discussed in Section III.5.

Figure 12:  a) Sample experimental spectrum with the best matched of a series
of synthetic spectra of mixed species plasma. b) Same experimental spectrum
and independent synthetic spectra of Ar, N, and O constituents illustrates
which observed lines belong to which species. These are from the same spectral
image in Fig. 6, after having subtracted the background. Figure 13:  Results
as obtained by the MCS, averaged over a set of 30 shots and binned into 3
$\mu$s intervals. a) Electron temperature determinations via PrismSPECT
comparison across several chords (separation from central chord in cm is
indicated). b) Fraction of Ar determined via PrismSPECT comparison. c)
Continuum emission levels, correlated with plasma density.

###  IV.4 High Resolution Spectroscopy

The high resolution spectrometer described in Section III.3 captures a finely
resolved profile of the Ar II 480.60 nm emission line. This profile shape
originates through a convolution of several mechanisms - the easiest of these
to analyze is the instrumental profile whose typically Gaussian shape is the
profile constituent originating from optical components, not the plasma
itself. Stark broadening manifests as a Lorentzian profile in response to the
electric microfield from electrons and ions in the vicinity of emitting ions,
and therefore scales linearly with the plasma density. Associated Stark widths
for different densities for this line are obtained in Ref. 30. The last
profile contribution is a composite effect from each jet conferring a Doppler
shifted profile with the previously mentioned broadening freatures due to the
projection of the jet’s radial velocity onto the spectral LOS.

To analyze the share of these attributes in the observed emission profile, a
technique was developed that models the incoming jets as cylinders of uniform
diameter and singular speed rather than a distribution of speeds. These
cylindrical jets intersect the instrument’s LOS which itself is approximated
as a narrower cylinder at an angle corresponding to the gun port location
relative to the collection optics port. As a result, jets originating close to
the collection optics port and close to the polar opposite location will
contribute a greater proportion of light to the overall profile because they
have a greater intersection volume, and will also be Doppler shifted the most
due to the shallow angle of jet with respect to optics LOS. Using this
framework, resultant composite profiles can be reconstructed for a set of
values of plasma bulk velocities and densities and seeing which best match the
observed data (bearing in mind that the simplicity of the analysis model will
contribute some uncertainty).

Figure 14:  High-Resolution profile analysis for a shot at 45.4 $\mu$s after
ejection with 1 $\mu$s exposure. a) Observed emission profile of Ar II 480.6
nm line, along with the best matching reconstructed profile (jet merge speeds
and density are indicated), a poor match assuming 50 km/s speeds, and the
instrumental profile. b) Individual profiles for the best match and amplitude
scalings from each jet based on angle with respect to collection optics. c)
Contour map of goodness-of-fit factors for a set of modeled merge densities
and velocities - the lower value indicates better matching.

Carrying out this analysis on a shot very near stagnation time, the results
are given in Fig. 14. Subfigure a. shows the experimentally observed profile,
the reconstructed profile with the indicated parameters, and the instrumental
profile obtained by looking at the H$\beta$ emission line using a low pressure
discharge hydrogen lamp. Subfigure b. indicates the individual component
profiles corresponding to each jet - note the varying amplitude and Doppler
shifts depending on the gun’s placement relative to the collection optics.
Subfigure c. shows the quality of match between the reconstructed profile and
the experimental one (lower values indicate better matching) as a function of
model parameters of jet speeds and plasma density. A particularly interesting
result is that to capture the observed profile, we must reconstruct using
velocities about 20 km/s or less, much less than our ejected jet velocities.
Indeed, using a velocity closer to the ejection velocities of 50 km/s produces
not only a profile which tends to be too broad, but also is double-peaked with
a valley in between (see purple curve in Fig. 14), features not observed in
experimental data.

###  IV.5 Interferometry

Figure 15:  Line-integrated plasma density profiles as measured by laser
interferometry on a) single shot and b) average of $\sim$20 shots. Time zero
is aligned to average launch time of the plasma jets, compensating for shot-
to-shot jitter in trigger time.

Inspection of the interferometry traces on both individual shots and multi-
shot averages in Fig. 15 reveals several features. As the leading edge of the
jets arrive, a slow increase of density is observed, preceding a sharp
increase on the central chord. At later time, similar sharp increases are
observed on the off-radial chords. In comparison with the experimental images
in Fig. 8, it is clear that the sharp increase is connected to the formation
of the central expanding luminous region, which is the collisional stagnation
of the liner and subsequent expansion / rebound of the stagnated liner plasma.
The paired chords display decent symmetry within shot-to-shot variation on the
early time rise of the density, with variations becoming observable on the
rebound in both magnitude and timing of the rebound arrival. This is likely
indicative of a small systematic asymmetry in the jet-to-jet delivered mass
and pressure, leading to the observed asymmetry in the rebound over many
shots. Spatial and temporal behavior of electron density determined from MCS
continuum intensity, as shown in Fig. 16, are in general agreement with that
determined via interferometry, and the time of peak density corresponds well
with the bright stagnation time seen in Figs. 7 and 8.

Figure 16:  LOS-integrated electron density from interferometry (left axis)
and MCS (right axis) both for their respective chord through chamber center.
The latter is obtained as the square root of the MCS continuum in Fig. 13.

##  V Discussion

###  V.1 Liner Uniformity

A major question in PJMIF is whether a sufficiently smooth and uniform
spherical liner can be formed from the merging of discrete hypersonic jets,
without significant density perturbations from shock waves between the merging
jets. The inertial fusion field in particular has encountered many
manifestations of the Rayleigh-Taylor instability when attempting liner
implosions, and found in all cases that smooth liners and shells of the utmost
uniformity are essential to avoid enhanced instability growth.

In previous PLX studies of obliquely merging jets in pairs, trios, and
clusters of 6 and 7 PLX plasma guns, inter-jet shocks along the merge plane of
different jets were frequently observed, whereas it appears largely absent in
the present experiment. This key difference is consistent with the former
experiments typically exhibiting slower velocities and shallower mean merge
angles between adjacent jets. In Ref[20] it was found that when gun angular
separations were increased from 11.6 to 20.5 degrees half-angle,
interpentration length exceeded ion mean free path length and thus shock
formation was substantially mitigated. In Ref[21] significant improvements to
jet-jet mass uniformity and modest improvements to velocity uniformity were
implemented. Measurements of the merger of clusters of 6 or 7 jets indicated
increased temperature and ionization, but could potentially still remain in
the desired interpenetrating regime without shock formation.

In the present experiment, the mean separation angle $\bar{\alpha}$ between
adjacent jets of 36 degrees constitutes the primary reason for not observing
the inter-jet shocks observed in prior experiments, since their merge velocity
$v_{m}=v_{j}sin(\bar{\alpha})$ is greater for larger angles. The
characteristic ion-ion interpenetration length is given by:

$L_{ii,s}=\sum_{i^{\prime}}\frac{v_{i}}{4\nu_{ii^{\prime},s}}$ (5)

in which $\nu_{ii^{\prime},s}$ is the slowing frequency through ion-ion
collisions, given by:

$\nu_{ii^{\prime},s}=$9\text{\times}{10}^{-8}$\lambda_{ii^{\prime}}\bar{Z}^{2}\bar{Z}^{\prime
2}\Big{(}\frac{1}{\mu}+\frac{1}{\mu^{\prime}}\Big{)}\frac{n_{i^{\prime}}\mu^{1/2}}{\epsilon^{3/2}}$
(6)

where $\lambda_{ii^{\prime}}$ is the Coulomb logarithm between
counterstreaming ions $i$ and $i^{\prime}$, $\bar{Z}$ is the mean charge
state, $\mu$ is the ion/proton mass ratio, $\epsilon$ is the energy associated
with velocity $v$, in units of eV, and $n$ is density in cm-3. If ions $i$ and
$i^{\prime}$ are of the same element (argon in this case), then the
interpenetration length $L_{ii,s}$ scales as
$v_{i}^{4}/n_{i^{\prime}}\bar{Z}^{4}$. As such, the velocity, merging angle,
and charge state of the jets exert a large control over the degree of
interpenetration.

If plasma-jet-driven liner implosions are scaled up to greatly increased
plasma density, one can expect decreased jet interpenetration and re-emergence
of collisional shock waves between the primary plasma jets. Due to the strong
$v_{i}^{4}$ dependence of interpenetration length on velocity, increases in
jet velocity concomitant with increases in liner density would have offsetting
effects, resulting in the persistence of significant interpenetration even at
many orders of magnitude greater energy densities. The exact termination point
of this scaling is not empirically known, but we conjecture that it will at
maximum end with densities corresponding to the onset of optical thickness of
the liner plasma, inhibiting effective radiative cooling of the liner and
leading to an increase in liner average charge state $\bar{Z}$. Ultimately,
this chain of events may lead to a relatively rapid onset of the liner
collisionality occurring at a threshold in parameter space. Future work may
shed light on these and other detailed aspects of the jet merging and
convergence phase and how they may be affected when scaling towards fusion-
relevant conditions. The current experiment effectively provides a single
encouraging data point showing that a liner free of primary shock waves can be
assembled at these conditions.

###  V.2 Comparison to Hydrodynamic Simulation

Figure 17:  Results from smooth-particle hydrodynamic simulation of the PLX
36-jet liner experiment using SPFMax code with ion slip model enabled.
Observed spatial structure and radially-averaged plasma density at stagnation
are in broad agreement with experimental observations (c.f. Figs. 7, 14, 15.)

The experimental campaign is compared to smooth-particle hydrodynamics (SPH)
simulations performed with the SPFMax code at UAH [31]. Simulations to date
have been performed with uniform nominal jet initial conditions of density and
velocity profile, not accounting for individual or shot-to-shot variations
between jets. No effects of any residual magnetic field are included in the
simulations (consistent with the cold dense jets being largely unmagnetized
post-flight). An ion-slip model is used to account for the effects of kinetic
interpenetration, leveraging the particle-based mechanics of the SPH code –
collisional interaction between fluid particles is adjusted by a multiplying
factor based on equation 6, with the effects that particles of high relative
velocity experience little collisional interaction, and vice versa. Results of
stagnation density profile with the ion-slip model turned on are shown in
Figure 17, showing similar morphology to the experimental imaging and inferred
density profiles. It is observed that simulation results with ion slip model
turned on agree much more closely with the experimental results, re-enforcing
the view that interpenetration is playing a strong role in high velocity liner
formation.

###  V.3 Liner Ram Pressure

We can infer bounds of liner peak ram pressure ($\frac{1}{2}\rho v^{2}$) by
combining the initial jet velocities measured from photodiodes ($V_{PD}$) for
the upper bound velocity, and high-resolution ($V_{S}$) spectroscopy for lower
bound velocity, plasma density $n_{e}$ from interferometry, and $\bar{Z}$ from
MCS results to obtain $\rho=m_{Ar}(\frac{n_{e}}{\bar{Z}})$. To estimate
$n_{e}$ from interferometry we take the peak line-integrated value of about
$2.0\text{\times}{10}^{18}$ cm-2, over the apparent domain that imaging
indicates to be brightest - around 15 cm. Thus the upper bound of ram pressure
is about 123 bar, and the lower bound is about 20 bar. This level is
consistent with modeling predictions that have incorporated the present jet
lengths of $\sim 30$ cm and moderate Mach numbers $\sim 10-20$, revealing that
there is a significant loss in liner density and ram pressure incurred due to
the volumetric expansion of the individual jets en route to the liner merging
radius, as well the extended length of the individual jets. If a thinner liner
with sharper radial density profile can be formed, possibly by use of jets
with higher Mach number and optimized launch velocity profile, the ram
pressure has potential to be increased by many orders of magnitude at a given
energy scale. Another path to increasing liner ram pressure and energy density
is to simply decrease the liner standoff distance, effectively making the
chamber smaller and starting the jets at a lesser radius. While this is
attractive for the liner performance, it puts increased demands on the
eventual system components to survive in a harsher fusion heat and radiation
environment, and may complicate reactor engineering [32].

##  VI Conclusions

The present set of experiments at PLX delivers the most substantial
experimental measurements to date to investigate the feasibility of the PJMIF
liner formation approach. Spatial and temporal measurements are obtained of an
argon liner formed via the merger of 36 discrete plasma jets, following the
liner evolution through jet launch, merging, spherical convergence,
stagnation, and rebound. Notably, conditions of moderate interpenetration
between primary jets are observed to lead to the absence of dense primary
shock structures in the early liner, allowing increased density uniformity to
be achieved. If primary shock waves are mitigated in this way, it seems that
arbitrarily smooth liners may be able to be formed with corresponding
improvements in primary jet parameters and control. A clear transition from
initial kinetic interpenetration to collisional interaction is observed, in
accordance with theoretical expectation. The obtained diagnostic measurements
also provide achieved absolute parameter values of ram pressure, stagnation
density, and temperature, useful for benchmarking computational models and
understanding the scaling of plasma liners to increased energy density. The
results provide a first singular data point for these benchmarking purposes –
future experiments could seek to verify theoretical liner scalings by
exploring the effect of perturbations to liner parameters.

###### Acknowledgements.

The authors would particularly like to thank Tom Byvank, Edward Cruz, Levi
Grantz, Ricardo Martinez, and many others who have contributed greatly to the
current experiments and overall PLX project, as well as the pioneers of the
PJMIF concept and PLX experiment, Francis Thio and Scott Hsu, respectively.
The information, data or work presented herein was funded in part by the
Advanced Research Projects Agency-Energy (ARPA-E), U.S. Department of Energy
under Award Numbers 20/CJ000/03/02 and DE-AR0001268, BETHE program. The views
and opinions of authors expressed herein do not necessarily state or reflect
those of the United States Government or any agency thereof. This work was
supported by the U.S. Department of Energy in part through the Los Alamos
National Laboratory. Los Alamos National Laboratory is operated by Triad
National Security, LLC, for the National Nuclear Security Administration of
U.S. Department of Energy (Contract No. 89233218CNA000001).

## Data Availability

The data that support the findings of this study are available from the
corresponding author upon reasonable request.

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