7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Compressible Theory of Unmagnetized Islands in Inhomogeneous Plasma
S. Cancino and J. Martinell,1 F.L. Waelbroeck and R. Fitzpatrick2
1Universidad Nacional Autonóma de México, Mexico
2
Institute for Fusion Studies, Univ. Texas at Austin, Austin, USAe-mail (presenter): Francois.Waelbroeck@austin.utexas.edu
Plasma inhomogeneity can create magnetic islands
through instabilities such as the classical, micro-tearing
and neoclassical tearing modes (TM, MTM and NTM).
Plasma inhomogeneity also affects how the plasma
responds to applied resonant perturbations, such as thoseused for ELM control in tokamaks and for creatingisland divertors in stellarators. The IslET fluid model(Island Equilibrium and Transport) [1] describes islands
in inhomogeneous plasma. It has recently been extended
to account for ion compressibility, which allows island
chains to couple to drift-acoustic waves. The
compressible IslET model completes the equilibrium
solution of Smolyakov et al. [2] by using transport
equations to specify the relaxed form of the profiles(density, velocity and current) and in particular thedegree to which they are flattened in the island.
Analytic solutions of the IslET model will be presented
in the semi-collisional “unmagnetized” regime. This
regime is such that island half-width W is wider than thewidth of the current channel found in linear theory but
narrower than the ion-acoustic gyro-radius, W<rs, with
rs= cs/ wci. It is also called the “supersonic” regime [3]because its islands have an azimuthal phase velocity thatexceeds the speed of ion-acoustic waves, w*>k||cs. The
new solutions extend a previous analysis [3] byremoving the assumption that the phase velocity of theisland is close to the electron drift velocity. This
assumption can be violated in cases of interest, such as in
the presence of temperature gradients or for islands
interacting with external structures such as resistivewalls, error fields, or other islands.
In the nonlinear regime, the evolution of a magnetic
island resulting from a tearing mode is governed by thegeneralized Rutherford equations describing the rates ofchange of its half-width W and propagation velocity V. It
is important for island models to describe both W and Vfor the following reasons:• The polarization current, which depends on V, isoften the dominant contributor to the island
drive, especially for thin islands;• The steady-state velocity can be a multi-valued
function of the plasma island width, in whichcase both may exhibit hysteresis.
The Rutherford equations are:dW/dt = 1.2 h D' + D(W,V);
dV/dt = F(W,V),
where h is the plasma resistivity in the tearing layer, D'and D(W,V) parametrize the drive for the tearing modecoming from respectively the external and internalcurrent and pressure distributions, and F(W,V) represents
the lateral force acting on the magnetic island. The IslET
model calculates the two functions D(W,V) and F(W,V)
for steady state islands, or for islands such that W and V
are constant. Equivalently, it calculates the external drive
parameter D' required for saturation of a tearing mode in
the nonlinear regime. The model has contributed to theunderstanding of island evolution by clarifying thecauses and effects of island magnetization and density
flattening, accounting for the decrease of the island
propagation velocity from the unmagnetized to themagnetized regime as well as the role of coupling to thedrift wave and the effect of the electron temperature
gradient on the island stability.
A limitation of previous versions of the IslET model [1],however, is its neglect of the ion parallel velocity. This
results in an incompressible description of the ion fluid
and suppression of the ion-acoustic or sound wave. In thelinear regime, coupling to the sound wave is known to be
responsible for the flattening of the density inside theisland and the accompanying reduction in the island
propagation velocity when its width is such that k||cs>>w* (or W>> rs Ls/Ln). By reducing the relative velocity
between the island and the surrounding ions, it also has astabilizing effect through the polarization current.
*This research was funded by grants PAPIIT-IN110021
and Conacyt A1-S-25157. Two of us (FW and RF) werefunded by the Office of Fusion Energy Sciences of theU.S. Department of Energy under Grant
DE-FG02-04ER54742.
References[1] FL Waelbroeck, Phys. Rev. Lett. 95, 035002 (2005).
[2] A. I. Smolyakov, H. R. Wilson, M. Ottaviani, and F.
Porcelli, Plasma Phys. Control. Fusion 46, L1 (2004).
[3] R Fitzpatrick and FL Waelbroeck, Phys.
Plasmas 15, 012502 (2008)