# On the genesis and nature of Palm Tree Modes in the JET tokamak

C. Maszl1,2, V. Naulin3, R. Schrittwieser2 and JET EFDA Contributors† 1
Funding Support and Industry Relations, TU Wien, Austria
2 Institute for Ion Physics and Applied Physics, University of Innsbruck,
Austria
3 PPFE, Department of Physics, DTU, DK-2800 Kgs. Lyngby, Denmark
<EMAIL_ADDRESS>
###### Abstract

Long-lived, highly localized structures called palm tree modes (PTM) are
observed in the edge plasma of the JET tokamak. Although PTMs are well
documented, little is known about the mechanisms which produce these
structures. In the case of the PTM, an ELM-postcursor, its genesis is usually
explained by ergodisation of the magnetic field due to edge localized modes
and the appearance of a seed magnetic island which evolves into a PTM later.
In this study we try to invoke a creation mechanism based on the concepts and
observations in edge plasma turbulence. An interesting aspect of plasma
turbulence is the occurrence of coherent, long-lived structures in the scrape-
off-layer (SOL). These localized and magnetic-field-aligned regions with
higher or lower plasma densities are called blobs and holes. Measurements show
that these filaments carry parallel currents. We thus here interpret ELM-
filaments as massive blobs and the interspace between these filaments as
holes.
We demonstrate that a forward-modelled closed current filament on a $q=3$
surface produces similar magnetic fluctuations as measured by the JET in-
vessel magnetic pickup coils if a PTM is present. From that we deduce that if
a hole is captured on a $q=3$ surface after an ELM-crash, a PTM equivalent
signature is generated. If the ELM-filament itself is captured on a $q=4$
surface, a signature equivalent to an outer mode appears.

##  1 Introduction

There is evidence for the existence of coherent long-lived highly localized
structures in the edge of tokamak plasmas. These are found for example in the
edge of JET as confined current ribbons or filaments (outer modes) [1] and
palm tree modes (PTM) . Although these phenomena are well documented, little
is known about the mechanisms which produce these structures. In the case of
the PTM its genesis is usually explained by ergodisation of the magnetic field
due to the ELM and the appearance of a seed magnetic island which evolves into
a PTM [2].
Here we try to invoke a creation mechanism based on the concepts and
observations of plasma turbulence. Turbulence in tokamaks is an active field
of research and great efforts are spent, experimentally and theoretically, to
quantify and understand particle, energy and momentum transport [3, 4]. An
interesting aspect of plasma turbulence is the occurrence of coherent, long-
lived structures in the SOL. These localized and magnetic-field-aligned
regions with higher or lower plasma densities are called blobs and holes,
respectively.They lead to intermittent transport through the scrape off layer
(SOL), which can effect the integrity of plasma facing components. Blobs and
holes were observed first by Zweben in 1985 during studies of edge density
turbulence with an array of Langmuir probes in the Caltech research tokamak
[5]. In the poloidal plane, blobs and holes look like drifting quasiparticles.
In the last years the origin of localized filamentary blobs has been
identified as the edge shear layer, where zonal-flows shear off meso-scale
coherent structures [6]. These filaments carry parallel currents [7]. A
significant amount of radial transport (up to $60\%$) might be carried by
blobs [8].
ELM filaments, as observed with fast camera diagnostics [9], show certain
similarities with blobs in plasma turbulence. Despite their size ELM filaments
are likewise current carrying, magnetic-field-aligned coherent structures [10]
with higher densities and excess temperatures [11], compared to the background
plasma. According to [12], ELMs should leave current holes behind because of
total current conservation on short time scales in the torus. These
observations lead us to the central hypothesis of this paper, that ELMs create
current and density holes in the edge plasma and that their motion can lead to
phenomena like PTMs.

##  2 Experimental results

The palm tree mode is an ELM post-cursor which was, as far as we know, only
observed in JET. It occurs in a wide variety of plasma conditions, as long as
the $q=3$ is located in the ELM-perturbed region. PTMs can be studied with the
electron cyclotron emission (ECE), soft X-ray diagnostic (SXR) which covers
the edge plasma and magnetic diagnostics at the limiters and the first wall
[2]. Figure 1 depicts a sliding window fast Fourier spectrum of a PTM magnetic
signal and its characteristic appearance (JET pulse: #73568, $t_{0}=12.995$
s).

Figure 1: FFT of a PTM measured by coil PP803 from the poloidal limiter array
(JET pulse: $73568$, $t_{0}=12.995$ s). The size of the FFT windows is
$\tau=2$ ms and the time shift between the windows $dt=64$ $\mu$s.

The PTM starts after the ELM crash at $t_{0}=12.995$ s. Because of the strong
magnetic perturbations of the ELM the actual onset time of the PTM cannot be
deduced with certainty. Characteristic features are an increase in frequency
for the first ms and the observation of rich harmonics, which indicate strong
localization of the feature. These characteristics can also be observed in ECE
and SXR signals and are the inspiration for the flowery name. The amplitude is
decaying with time. Typical lifetimes of PTMs are around 23 ms although PTMs
with lifetimes up to 60 ms can be observed. If an ELM is triggered during a
PTM event, the PTM is terminated immediately.

JET has a number of in-vessel magnetic coils with sample frequencies in the
range between one and two MHz. These coils and coil arrays were used to study
the helical structure and localization of the PTM as well as growth and decay.
The ECE diagnostic was used to study temperature perturbations. The
combination of both diagnostics allowed a rough estimate of the location.
Furthermore, charge exchange recombination spectroscopy (CXRS) was used to
correlate the rotation frequencies of PTMs with the edge rotation. For this
study a PTM database was created containing 36 PTMs. 24 of them are not
superposed by other MHD activity (see Appendix Tab. 3 and Tab. 4 for more
details). This is important because other MHD activity would modulate PTM
signals and circumvent the study of growth and decay behaviour. PTMs were
searched which are not stopped by a subsequent ELM, which limit the lifetime,
to allow investigations on dissipative processes. For two PTMs the diagnostic
coverage was more extensive (JET pulse: #52011111Session Aims: Influence of
triangularity on confinement, pedestal and SOL parameters $t=19.14-19.22$ s ,
#73568222Session Aims: Scaling of confinement and pedestal with rho*, beta
$t=12.8–13.2$ s). Aside from fast magnetics also fast ECE with higher time
resolution ($f_{s}=250$ kHz) was available. Therefore, these two pulses were
studied in more detail. The JET control room physics summary is presented in
Tab. 1

Table 1: JET Control Room Physics Summary for the pulses #52011 and #73568. $B_{t}$ toroidal magnetic field, $I_{p}$ plasma current, $n_{e}$ electron density, $T_{e}$ electron temperature, $P_{NBI}$ neutral beam injector power, EFCC error field correction coils, - not available/applicable Pulse |  $B_{t}$(T) |  $I_{p}$(MA) |  $n_{e}dl$($10^{19}$m-2) |  $T_{e}$(keV) |  $P_{NBI}$(MW) | EFCC | Year
---|---|---|---|---|---|---|---
52011 | 2.67 | 2.51 | 17.5 | - | 11.8 | - | 2000
73568 | 2.00 | 2.20 | 12.4 | 4.6 | 10.7 | off | 2008

###  2.1 Rotation

Fourier spectra of PTMs show rich harmonics and also a frequency increase in
the first ms. It is known that ELMs cause momentum losses in the pedestal
region. These are usually studied with CXRS [13]. The rotation in figure 2
drops almost by $20$ krad/s after an ELM event.

Figure 2: Edge rotation as measured by CXRS. Recovery after ELM induced
momentum losses (vertical line) can be observed. Courtesy by Thijs W.
Versloot.

It was found that PTMs are co-rotating with the edge plasma [2]. Furthermore
the initial and final frequencies of PTMs and the pedestal are in the same
order of magnitude as this co-rotation [14]. A comparison is given in Fig. 3.
Here the initial frequencies are colour-coded red and the final frequencies
black. The solid line indicates unity.

Figure 3: Comparison of initial (Min) and final (Max) velocities of PTM (MHD)
and pedestal frequencies (CXRS) for single ELM data. The solid line indicate
unity. Courtesy by Thijs W. Versloot.

The frequency increase and hence toroidal angular velocity $v_{tor}$ in rad/s
of the PTM in JET pulse #73568 at $t_{0}=12.994$ s (Fig. 1) can be fitted by

$v_{tor}=m_{0}+m_{1}\Big{(}1-e^{-m_{2}t}\Big{)}.$ (1)

with the fit parameters $m_{0}=14816.5$ rad/s, $m_{1}=9235.7$ rad/s and
$m_{2}=189.4$ s-1. The initial and final frequencies as seen in CXRS and MHD
data are comparable. Surprisingly, the frequency increase extracted from MHD-
data is approximately one order of magnitude faster. This discrepancy has to
be addressed in future research.

###  2.2 Temperature perturbations

PTMs can also be seen in the signals of the ECE diagnostic. Surface plots of
ECE data locate the PTM in the gradient region of the pedestal (Fig. 4).
However, ECE data have to be considered with care because they rely on
equilibrium reconstruction. The exact spatial localisation of MHD modes is
therefore not straightforward [15].

Figure 4: The electron temperature $T_{e}$ as function of time $t$ and major
radius $R$, measured by ECE (KK3-CATS, JET pulse: $\\#52011$). The temperature
perturbations due to the PTM are visible in the edge region of the pedestal.

Moreover, the influence of the edge current density will alter the equilibrium
in the plasma edge. PTMs are capable to disturb the equilibrium locally which
is demonstrated in Fig. 5. There is a strong correlation and a $180^{\circ}$
phase shift between ECE channel B1:012 and coil T009 which is close to the
line of sight of the diagnostic.

Figure 5: Temporal comparison of a a) $\textrm{d}B/\textrm{d}t$ signal from
magnetic coil T009 (red) in octant 7 (JET pulse: $\\#52011$) and b) an
electron temperature signal (ECE B1:012, black). Both signals $S$ are
normalised to $1$.

This is another direct evidence of a current perturbation due to the PTM. A
similar observation was made by Koslowski et al. They found that the PTM has a
tearing mode structure [2]. The distance of the PTM to coil PP804, slightly
below the mid-plane on the outboard limiter, is approximately $0.19$ m.

###  2.3 Helical structure and decay of the PTM

Typical application areas of the JET in-vessel magnetic coils are plasma
control, equilibrium reconstruction and, with the fast arrays, the study of
MHD phenomena just to name a few. Fast coil arrays are also used for MHD mode
number analysis and hence to infer the periodicity of these signals. This was
also done with PTM data by Koslowski et al. [2] in the past. They concluded
that the PTM has a tearing mode structure and is formed in the vicinity of a
resonant $q=3$ surface.

A complementary novel approach to infer the periodicity was performed by B.
Lagier et al. [16]. The available in-vessel magnetic coils were used to infer
the helical structure by a comparison with a synthetic signal in the
toroidal/poloidal plane. At first the magnetic signals were calibrated,
numerically integrated and digitally filtered by a second order Butterworth
high-pass filter with a cut-off frequency of 1 kHz. Afterwards the probe
position were indicated in the toroidal/poloidal plane and the signal strength
was colour-coded. If the perturbation of the PTM is close to one coil, the
signal strength was high an therefore color-coded in red. Weak signals are
color-coded blue. The results are presented in Fig. 6.

Figure 6:  The figure is based on a JET report of Benjamin Lagier [16] and
simplified for clarity. The figure shows four different time steps. Each plot
is organized in three sections. In the upper left corner is the representation
of a field line (blue) with constant $q=3$ on a rational surface for a torus
with circular cross-section. The window in the upper right corner shows a
measured signal from a fast coil in JET. Maxima are marked with red dots. The
black vertical dashed line is a time marker. The lowest window represents the
toroidal/poloidal plane. Limiter coil arrays on the high field side (HFS) and
on the low field side (LFS) are indicated by HFS and LFS for easier
orientation. Every used coil is represented as a rectangle where the measured
signal strength is color-coded (red$\widehat{=}$high, blue$\widehat{=}$low
signal strength). Green lines indicate the location of the simulated field
line on a $q=3$ surface, synchronized with the measured signals (JET pulse:
#77188, $t=10.9045-10.9080$ s).

The green lines in Fig. 6 are a representation of a field line on a $q=3$
surface for a tokamak with circular cross-section. Once the simulated filament
is synchronized with the experimental data, the highly localized simulated
filament propagates in phase with the measured current perturbation of the PTM
through the toroidal/poloidal plane. If the simulated filament is close to a
coil also the measured signal is high. That is another evidence for the high
localization of the PTM.

It is also instructive to compare the envelopes of the filtered and integrated
PTM signals from magnetic coils at different positions around the torus in one
poloidal plane (Fig. 7, JET pulse: $\\#73568$, $t_{0}=12.9936$ s). At the
inboard side (Fig. 7, coil I802) the mode grows for the first ms starting
close at zero and decays after this phase almost linearly. Since ELM
perturbations are more pronounced for the outboard side, the onset of the PTM
can be traced back almost right after the ELM. The behaviour is different at
the outboard side. Above the mid-plane (coil PP801) the onset of the mode is
not as clear as at the inboard side since strong perturbations following the
ELM-crash prevail. After this phase, two decay time constants can be
identified. At first, the PTM shows a rapid decay phase (A) followed by a
linear decay phase (B). Below the mid-plane (coil PP805) the amplitude rises
quickly, peaks and after that process decays also with two time constants. In
principle this could also be explained by a shift of the whole plasma from the
inboard to the outboard side. But the behaviour of the signal as measured by
PP805 verifies why a movement of the whole plasma cannot cause this process.
It would have to include also a rotation of the hole plasma in the electron
diamagnetic drift direction to induce this signal.

Figure 7: Comparison of filtered and integrated magnetic signals at the
outboard and inboard side of JET for three different coils (JET pulse:
$\\#73568$, $t_{0}=12.9936$ s). The envelopes of the signals are indicated
with the red lines. (A) and (B) in the upper right panel indicate two time
constants in signal decay.

Summarising, this spatio-temporal investigation of this PTM shows the best
results because the PTM is located close to the in-vessel coils. PTMs are
apparently highly localized structures (Fig. 6), which are co-rotating with
the bulk plasma (Sec. 2.1) and show a temporal evolution that corroborates its
generation at the outboard side (Fig. 7).

##  3 Forward modelling of magnetic fluctuations

From these experimental results we conclude that it should in principle be
possible to describe the PTM phenomenology as rotating closed current filament
in the pedestal region where an initially localised current distribution is
allowed to expand parallel to the magnetic field on a rational surface.
Following the approach in [17], Biot-Savart’s law was used to compute the
magnetic field at different coil positions and times. The helical structure of
the filament was obtained for a single field line on a rational $q=3$ surface
with FLUx Surface Handling (FLUSH) [18]. It is a collection of FORTRAN
routines to assist in reconstructing and post-processing the flux solution of
a plasma equilibrium solver at JET. To be more specific in this study the
subroutines FLUQAX and FLUPN3 were used for JET pulse: $\\#73568$ at $t=12.98$
s. The angular velocity of the filament was mimicked using Eq. 1. The distance
of the mode $d\approx 0.19$ m to the pick-up coil PP804 was estimated using
the radial position information from the ECE diagnostic (Fig. 4).
As initial condition a Gaussian shaped current density distribution along the
parallel direction of the field line with a maximum current density of
$j_{0}=4.2\times 10^{5}$ A/m2, standard deviation $\sigma=$1.2 m and a
filament cross-section of $A_{0}=1.8\times 10^{-3}$ m2 was placed in the
middle of the domain at $t_{0}$. This peak current density - giving a peak
magnetic field strength - was matched with the maximum field for coil PP801 in
Fig. 7.

In order to limit the lifetime of the modelled filament to $t_{lt}=25$ ms a
dissipation mechanism is required. In this study we treat the filament as a
short solenoid with $N=3.0$ windings and a series resistance $R$. The
resistance is determined via the parallel Spitzer resistivity
$\eta_{\parallel}$ and the length of a filament $l_{f}$ on a $q=3$. In the
case of JET this is approximately $l_{f}=56$ m. The electron temperature at
the location of the PTM after the collapse of the pedestal is roughly
$T_{e}\approx 280$ eV. The parallel Spitzer resistivity is therefore around
$\eta_{\parallel}=7.0\times 10^{-8}$ $\Omega$m and the Ohmic resistance
therefore $R=3.9\times 10^{-6}$ $\Omega$.
The inductance $L$ of a short solenoid is computed according to [19]

$L(\mu_{r})\approx\mu_{0}\mu_{r}\frac{N^{2}A}{h_{f}+0.8r_{f}}$ (2)

where $h_{f}=3$ m is the length, $r_{f}=4$ m the radius of the solenoid and
$A=\pi r_{f}^{2}$ the area of the cross-section. The time constant for the
current decay is $\tau=L(\mu_{r})/R$. We assume that the current is gone after
five time constants $\tau=t_{lt}/5=0.005\,$s. With $R=3.9\times 10^{-6}$
$\Omega$ and $\tau=0.005$ s we compute for the inductance $L$ and the relative
permeability $\mu_{r}$

$L=1.98\times 10^{-8}\,\textrm{H}\qquad\mu_{r}=0.23\times 10^{-3}.$ (3)

For the numerical simulation with a time resolution of $1\times 10^{-7}$ s,
periodic boundaries where chosen to reflect the nature of a closed current
filament (Fig. 8).

Figure 8: Illustration of a filament with locally varying $q$ on a $q=3$
surface, calculated with FLUSH in various presentations. The lower right panel
shows the current density $j$ of the filament in parallel direction $p$. The
colored squares in the two upper panels represent the magnetic pick-up coils
at the limiters in the octants four and eight. The current distribution after
$24$ ms in the filament is color-coded. Red means high current density, black
low current density. For the exact values see the lower right panel please
(Equilibrium from JET pulse: $\\#73568$, $t=12.98$ s).

###  3.1 Results

A comparison of FFTs from measured and integrated data (Fig. 1) and from
forward-modeled magnetic fluctuations (Fig. 9) show good agreement. Both plots
show the characteristic harmonics, a sharp increase of the frequency in the
beginning and a slow decay of the mode after approximately $25$ ms. Obviously,
a highly localized current filament is also capable to produce the observed
spectra.

Figure 9: FFT of magnetic fluctuations from a forward-modeled closed rotating
current filament.

Forward modelling of magnetic fluctuations gives information both on the
direction of the current and the periodicity of the current filament. The
current is approximately $I\approx-294.5$ A at $t=12.996$ s. The current
density is then of the order of $-0.15$ MA/m2 assuming a filament cross-
section of $A_{0}=1.8\times 10^{-3}$ m2 [2]. The polarity (sign) of the coils
was defined using the disruptions $\\#73460$, $\\#77176$, the $m/n=2/1$ mode
in $\\#77635$ ($t=44.207-44.2084$ s) and the dry run $\\#77638$ ($40-43$ s. P4
blip window) by Sergei Gerasimov et al333Private communication, [20]. The sign
of the current indicates a lack of current compared to the plasma current and
therefore a current hole in the PTM region.

The signals of magnetic signatures from an unipolar current filament are
comparable to the envelopes of the measured signals (Fig. 11 and Fig. 11). For
the coils PP801, PP803, PP805 the signal strength is overestimated. Although
fairly well synchronized with PP801, there is a small phase shift between the
signals in PP803 and PP805. This is even worse for signals at the inboard side
where the current is underestimated. Nevertheless the shape of the signals
approve the negative sign. Errors in the phase relation are probably due to
use of a poor equilibrium where the edge current and distortions of the PTM
are not reflected.

Figure 10: Comparison of a simulated unipolar current filament (red) with
signals from the inboard array (black, I801-I803) for JET pulse $\\#73568$.

Figure 11: Comparison of a simulated unipolar current filament (red) with
signals from the outboard array (black, PP801-PP805) for JET pulse $\\#73568$.

The presented model is simplified, therefore we expect only qualitative
agreement with the observations.

##  4 Discussion

Based on the results from the experiment an intuitive model is proposed which
could in principle explain the genesis of the PTM.

Langmuir probe measurements in JET reveal that blobs and holes are created in
the edge shear layer. Whereas blobs can propagate large distances and in
principle can reach the first wall, holes travel up the temperature gradient
and are only observed slightly inside the region where they have been born.
Calculations show that holes are filled on the conductive time scale
$\tau_{cond}$. Since $\tau_{cond}\approx L_{\parallel}/\chi_{e\parallel}$
depends on the parallel length $L_{\parallel}$ and the electron thermal
conductivity $\chi_{e\parallel}$, the lifetime of holes is in the range of
$\mu$s [6]. The lifetime of a hole is therefore influenced by its size and the
electron temperature. Additionally, low shear rates are a prerequisite.
Otherwise holes are sheared apart rather quick.
A localized, $B$ field aligned hole wich is travelling to a resonant magnetic
surface with a radial velocity $v_{R}$ exhibits a current, a density and a
temperature perturbation (Fig. 12a). It is expanding parallel to the field
line with velocity $v_{\parallel}$. Holes are usually quickly filled by
parallel $\Gamma_{\parallel}$ and perpendicular transport $\Gamma_{\perp}$.
Fig. 12b) shows the situation if such a hole was able to reach a field line on
a resonant surface. Then, the polarization is short-circuited by parallel
currents and the motion stops. The hole is then filled by perpendicular
transport only which increases its lifetime significantly.

Figure 12: a) A hole is generated between the $q=3$ and $q=4$ surfaces. The
localized, $B$ field-aligned, polarized hole travels up the density gradient
with the radial advection velocity $v_{R}$ and expands in parallel direction
with velocity $v_{\parallel}$. In this stage, it is filled by parallel
$\Gamma_{\parallel}$ and perpendicular transport $\Gamma_{\perp}$.
b) The hole was able to reach a field line on the $q=3$ surface before it was
completely filled and closed on itself. $v_{R}=0$ since the charge imbalance
is short-circuited by parallel currents. It is now filled by perpendicular
transport $\Gamma_{\perp}$ only.

Following that line of thought, plasma edge properties should have a large
impact on the lifetime and whether a PTM can be observed or not. In the
following section, a simple multi-machine comparison is presented for the
tokamaks ASDEX Upgrade, DIII-D, JET and ITER (Fig. 13).

Figure 13: Multimachine comparison of maximum radial propagation distances of
holes under the assumption that these holes are filled on density $\tau_{cs}$,
thermal $\tau_{the}$ and resistive $\tau_{ei}$ time scales. All corresponding
distances ($L_{cs}$, $L_{the}$ and $L_{ei}$) are normalized by the major
radius $R$ of the respective machine.

The radial advection velocity $v_{R}$ of the hole is assumed to be caused by
the nonlinear evolution of interchange motions, without any presumption of
plasma sheaths. Radial velocities and radial extensions are computed according
to the model in [21]. Sheath dissipative models like in [22] are not
appropriate in this case because of the high radial velocities of the
structures. The hole enters and leaves any given flux tube so quickly that the
plasma in the flux tube cannot react to the pressure perturbation [23]. The
particle density and the edge safety factor for ASDEX Upgrade, JET and DIII-D
were taken from [24]. The associated pedestal temperatures for H-mode plasma
with type-I ELMs were selected from [25]. The required information for ITER
was found in [26] and [27].
Figure 13 summarizes the maximum normalized propagation distances depending on
the filling mechanism. A hole with parallel length $L_{blob}$ [28] and radial
velocity $v_{R}$ can travel the distance $L_{cs}$ if it is filled by ions with
sound speed $c_{s}$. Similarly, distances can be calculated if the hole is
filled by thermal electrons (distance $L_{the}$) or if the current decays
according to the Spitzer resistivity (distance $L_{ei}$). The raw data and
calculations are summarized in the appendix in Tab. 5.
Holes can travel slightly further in ASDEX Upgrade and DIII-D on thermal
$\tau_{the}$ and density time scales $\tau_{cs}$ if compared to JET or ITER.
This is due to the lower pedestal temperatures for the smaller machines. The
strongest influence on the propagation distance is found on the resistive time
scale $\tau_{ei}$. Figure 13 shows that the collisionality in the pedestal has
the strongest influence on the lifetime of holes. Therefore, ITER is expected
to excel when it comes to lifetimes and propagation distances of holes.

From pellet injection experiments in DIII-D and Tore Supra it is known that
the maxima of the mass deposition profiles are close to the magnetic $q=2$ and
$q=3$ surfaces. Low order rational surfaces appear to slow down or even stop
the polarization drift of the density cloud towards the low field side of the
plasma [29]. Since holes are regions of lower density than the ambient plasma
the $\nabla B$ polarization and therefore the drift is in opposite direction
to blobs or density clouds. Additionally, it is similarly to expect that holes
can be slowed down or trapped in the vicinity of a rational surface. Under the
assumption that the interchange drive of a polarized ELM-induced hole moves it
into the proximity of a rational surface with low $q$, it could be slowed down
or even stopped. An illustration of an ELM in the exhaust phase is given in
Fig. 14. Holes are indicated as black filaments, ELM filaments are in white.
Large ELM induced holes could close on themselves in the vicinity of a
rational magnetic field line and therefore detach from the magnetic surface.
During this process a closed filament would be created. For a closed filament,
charge interchange imbalance would be short-circuited by parallel currents
which would stop the filament completely. The result would be a closed, well
localized filament with a significantly increased lifetime because it could be
only filled by slow-perpendicular transport. This filament should then have a
distinct and rational ratio of toroidal and poloidal periodicity. The lack of
current inside the filament would change the equilibrium locally there.

Figure 14: Illustration of an ELM in the exhaust phase at the outboard side of
a tokamak. If an ELM filament (white) is stopped and captured at e.g. the
$q=4$ surface (green) an outer mode or current ribbon could be created.
Similarly a hole (black) captured on a $q=3$ surface could create a PTM.

In our opinion a promising candidate for the described events above is the
Palm Tree Mode (PTM), an ELM post-cursor. As presented, forward-modeled
magnetic fluctuations from a current filament are in a fair agreement with
experimental results. The physical properties of PTMs are compatible with the
properties expected for holes after ELM-filaments are generated. The strong
influence of the collisionality in the pedestal on the lifetime of the holes
explain why PTMs are only observed in JET up to now (Fig.13). For ITER it is
expected that these phenomena will also be present and influence the
confinement in the edge region.
A candidate for trapped blobs are outer modes which are current filaments with
excess current on a rational surface [1]. Taking the proposed model into
account outer modes are ELM filaments, which were not able to propagate to the
scrape-off layer (SOL). If present, outer modes mitigate ELMs. In our view,
PTMs are remnants of ELM-induced holes. Both of these structures are born and
trapped in the vicinity of rational surfaces. Nevertheless, the probability to
create PTMs should be lower compared to outer modes because ELM induced holes
would have to travel up the temperature gradient into regions with increasing
parallel transport and could be filled before they can be trapped on a
rational surface.

##  5 Conclusion

This paper presented how the concept of blob and hole-like transport can
contribute to shed more light on the genesis and nature of Palm Tree Modes and
Outer modes in the JET tokamak. It was demonstrated that under the current
filament assumption it is possible to forward-model the magnetic signatures of
PTMs which shows the same harmonics structure and reflect also the signal
shapes reasonably well.
Additionally, it was demonstrated how the JET in-vessel magnetic coils can be
utilized to get more insights in the genesis and nature of PTMs.
In the introduction in Sec. 1 we raised the question whether ELMs create
current density and density holes in the edge plasma. Based on our findings we
suggest that PTMs are trapped current and density holes produced by ELMs. A
fruitful further direction of research could be whether or not L-mode blobs
and holes in ITER could be big enough to produce similar structures. This
could have implications on the L-mode confinement and the LH-transition.
We also conclude that the rich harmonics in FFTs are probably not due to MHD-
modes but rather because of the high localisation of the filament. FFT spectra
are therefore probably misleading in PTM analysis. Other tools like empirical
mode decomposition and Hilbert amplitude spectra therefore give a better
representation of the physical nature of the PTM [30].

##  6 Acknowledgements

This work has been carried out within the framework of the EUROfusion
Consortium and has received funding from the EURATOM research and training
programme 2014-2018 under Grant Agreement No. 633053. The views and opinions
expressed herein do not necessarily reflect those of the European Commission.
The support by the Austrian Science Fund (Fonds zur Förderung der
wissenschaftlichen Forschung in Österreich) under grant No. P19901 is also
gratefully acknowledged. Additional support was lend by the österreichische
Forschungsgemeinschaft (Austrian Research Community) under grant 06/11454,
International Communication.
One of the authors, Christian Maszl, wants to thank Codrina Ionita, Thijs W.
Versloot, Benjamin Lagier and Mathias Brix for valuable discussions and
support during his visits at JET and the DTU plasma physics group for their
hospitality.

## References

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## Palm tree mode database

PTMs where searched manually with the IDL program SPECVIEW at the JET Analysis
Cluster (JAC). Tab. 3 and Tab. 4 summarizes the palm tree modes found. The
second column gives the time windows where the PTMs appear. The abbreviation
TBE (terminated by ELM) indicates if the mode was stopped by a subsequent ELM
(y) or reached its unperturbed lifespan (n). The hyphen (-) marks inconclusive
cases. TW marks pulses were no fast time window is available. The columns ECE
and MAGS give the sample frequencies of the respective diagnostics. The MHD
section documents the fundamental frequencies of other MHD activity. The year
column allows a discrimination between the different divertor configurations
(Tab. 2).

Table 2: Divertor configurations in JET from 1999-2009. Period | Name | Abbrevation
---|---|---
1999-2001 | MkII Gas Box | MkII GB
2002-2004 | MkII Septum Replacement Plate | MkII SRP
2005-2009 | MkII High Delta | MkII HD
Table 3: Palm tree mode database - part I Pulse | t (s) | TBE | ECE | MAGS | MHD | Year
---|---|---|---|---|---|---
52011 | 59.14-59.22 | - | 250 kHz | 250 kHz | 39 kHz | 2000
58982 | 57.26-57.39 | y | 250 kHz | 250 kHz | 12 kHz | 2003
72299 | 61.44-61.48 | n | TW | 1 MHz |  | 2008
73568 | 52.80-53.20 | n | 250 kHz | 2 MHz | 39 kHz | 2008
73569 | 51.37-51.44 | n | TW | 2 MHz | 29 kHz | 2008
74812 | 54.56-54.64 | - | TW | 1 MHz | 11 kHz | 2008
74812 | 56.35-56.45 | n | TW | 1 MHz |  | 2008
75411 | 57.10-57.20 | n | TW | 1 MHz |  | 2008
75411 | 57.86-57.92 | n | TW | 1 MHz |  | 2008
76793 | 49.60-49.80 | - | TW | 1 MHz | 9 kHz | 2009
77184 | 53.35-53.40 | - | TW | 1 MHz | 32 kHz | 2009
77185 | 55.75-55.95 | n | TW | 2 MHz |  | 2009
77186 | 51.12-51.15 | y | TW | 1 MHz |  | 2009
77188 | 50.89-50.93 | y | TW | 1 MHz |  | 2009
77319 | 57.10-57.15 | y | TW | 1 MHz |  | 2009
77326 | 63.90-64.05 | n | TW | 1 MHz |  | 2009
77326 | 65.10-65.20 | n | TW | 1 MHz |  | 2009
77326 | 65.50-65.70 | n | TW | 1 MHz |  | 2009
Table 4: Palm tree mode database - part II Pulse | t (s) | TBE | ECE | MAGS | MHD | Year
---|---|---|---|---|---|---
77326 | 66.10-66.20 | n | TW | 1 MHz |  | 2009
77329 | 64.20-64.50 | n | TW | 1 MHz |  | 2009
77329 | 65.30-65.40 | n | TW | 1 MHz |  | 2009
77329 | 65.90-66.00 | n | TW | 1 MHz |  | 2009
77331 | 65.30-65.40 | n | TW | 1 MHz |  | 2009
77332 | 66.00-66.12 | y | TW | 1 MHz |  | 2009
77335 | 63.90-64.10 | n | TW | 1 MHz |  | 2009
77335 | 65.30-65.45 | n | TW | 1 MHz |  | 2009
77342 | 63.90-64.00 | n | TW | 1 MHz |  | 2009
77342 | 64.34-64.41 | n | TW | 1 MHz |  | 2009
78690 | 55.40-55.50 | n | TW | 1 MHz |  | 2009
78712 | 53.10-53.60 | n | TW | 1 MHz | 11 kHz | 2009
78712 | 55.40-55.70 | n | TW | 1 MHz |  | 2009
79619 | 57.25-57.35 | n | TW | 1 MHz | 13 kHz | 2009
79620 | 45.85-45.92 | n | TW | 1 MHz |  | 2009
79620 | 46.49-46.58 | n | TW | 1 MHz |  | 2009
79744 | 58.10-58.25 | n | TW | 1 MHz | 16 kHz | 2009
79745 | 61.10-61.30 | n | TW | 1 MHz | 26 kHz | 2009

## Multi-machine comparison

Tokamak | JET | ASDEX U | ITER | DIII-D |
---|---|---|---|---|---
$n$ (m-3) | $6.0\times 10^{19}$ | $6.0\times 10^{19}$ | $1.0\times 10^{20}$ | $6.0\times 10^{19}$ | particle density
$T_{e,i}$ (eV) | 1200 | 400 | 5000 | 700 | temperatures
$\ln\Lambda$ | 16 | 15 | 17 | 15 | Coulomb log.
$\eta_{\parallel}$ ($\Omega$m) | $2.0\times 10^{-8}$ | $9.8\times 10^{-8}$ | $2.5\times 10^{-9}$ | $4.8\times 10^{-8}$ | Spitzer res.
$R$ (m) | 3.1 | 1.65 | 6.2 | 1.69 | major radius
$q$ | 3.0 | 4.0 | 3.0 | 4.0 | safety factor
$B$ (T) | 2.3 | 3.0 | 5.0 | 3.0 | magnetic field
$\omega_{ci}$ (Hz) | $1.1\times 10^{8}$ | $1.5\times 10^{8}$ | $2.4\times 10^{8}$ | $1.5\times 10^{8}$ |  $i^{+}$ gyro freq.
$c_{s}$ (m/s) | $3.4\times 10^{5}$ | $2.0\times 10^{6}$ | $6.9\times 10^{5}$ | $2.6\times 10^{5}$ | sound speed
$v_{the}$ (m/s) | $2.1\times 10^{7}$ | $1.2\times 10^{7}$ | $4.2\times 10^{7}$ | $1.6\times 10^{7}$ |  $e^{-}$ thermal vel.
$\rho_{s}$ (m) | $3.1\times 10^{-3}$ | $1.4\times 10^{-3}$ | $2.9\times 10^{-3}$ | $1.8\times 10^{-3}$ |  $i^{+}$ gyro rad.
Blob
$L_{blob}$ (m) | 2.4 | 1.7 | 4.9 | 1.8 | parallel length
$\Delta n/n$ | 0.5 | 0.5 | 0.5 | 0.5 | perturbation
$R_{blob}$ (m) | $1.1\times 10^{-2}$ | $5.7\times 10^{-3}$ | $1.2\times 10^{-2}$ | $7.2\times 10^{-3}$ | radial blob size
$v_{blob}$ (m/s) | $2.0\times 10^{4}$ | $1.2\times 10^{4}$ | $3.1\times 10^{4}$ | $1.7\times 10^{4}$ | blob velocity
Timescales
$\tau_{cs}$ (s) | $7.2\times 10^{-6}$ | $8.8\times 10^{-6}$ | $7.0\times 10^{-6}$ | $6.8\times 10^{-6}$ | $L_{blob}/c_{s}$
$\tau_{the}$ (s) | $1.2\times 10^{-7}$ | $1.5\times 10^{-7}$ | $1.2\times 10^{-7}$ | $1.1\times 10^{-7}$ | $L_{blob}/v_{the}$
$\tau_{ei}$ (s) | $3.0\times 10^{-4}$ | $6.1\times 10^{-4}$ | $1.4\times 10^{-4}$ | $1.2\times 10^{-5}$ | $ne^{2}/m\eta_{\parallel}$
Propagation
$L_{cs}$ (m) | 2.4 | 1.7 | 4.9 | 1.8 | $v_{blob}\cdot\tau_{cs}$
$L_{the}$ (m) | $2.4\times 10^{-3}$ | $1.7\times 10^{-3}$ | $3.6\times 10^{-3}$ | $1.9\times 10^{-3}$ | $v_{blob}\cdot\tau_{the}$
$L_{ei}$ (m) | 0.6 | $7.0\times 10^{-2}$ | 4.4 | 0.2 | $v_{blob}\cdot\tau_{ei}$
Table 5: Multimachine comparison for characteristic blob sizes, timescales and
propagation estimates.