title: Instability of twisted magnetar magnetospheres
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stars: magnetars – magnetic fields – methods: numerical – stars: neutron – X-rays: bursts

Introduction {#sec:introduction}
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Soft gamma-ray repeaters (SGRs) are neutron stars with recurrent X-ray activity in the form of short bursts with duration $\sim 0.1$s and luminosities in the range $10^{36}-10^{43}$ergs$^{-1}$. Over the last 40 years, three bursts have been uniquely energetic, the so-called [*giant flares*]{} (GFs) with luminosities of the order of $10^{44}-10^{47}$ergs$^{-1}$ [SGR0525-66, SGR1900+14 and SGR1806-20, see @Cline1980; @Hurley1999; @Hurley2005]. In the three referenced cases, a short initial peak was followed by a softer X-ray tail lasting for $50-400$s. The engine behind these extraordinary events are [*magnetars*]{}, neutron stars with the strongest known magnetic fields [$10^{14}-10^{16}$G; see comprehensive reviews of magnetar observations and physics, e.g. in @Woods2006; @Rea2011; @Turolla2015; @Mereghetti2015; @Kaspi2017].

The precise mechanism producing such energetic events is still unclear. Strong magnetic fields are a gigantic energy reservoir in magnetars, generally of the order $$\begin{aligned}
{\mathcal{E}}_{\rm magnetar} \sim 1.6\times 10^{47} \,\text{erg}\,\left ( \frac{B}{10^{15}\,\text{G}}\right )^{2}\left ( \frac{R_*}{10\,\text{km}}\right )^3,\end{aligned}$$ where we consider a neutron star with radius $R_*$.

The timescale on which the magnetar is evolving, mainly due to Hall drift and Ohmic dissipation in the crust, is 