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approvedrealfreqtmodes_sherwood18_upload.pdf2018-05-08 10:53:38Andrew Cole


Author: Andrew J. Cole
Requested Type: Poster
Submitted: 2018-02-28 16:19:12

Co-authors: J. M. Finn, D. P. Brennan

Contact Info:
Columbia University
116th St & Broadway
New York, NY   10027

Abstract Text:
We present recent investigations[1] of tearing modes in various
single-fluid (resistive MHD) regimes, indicating real frequencies over
a wide range of parameters. Specifically, we first show the
resistive-inertial (RI) and viscoresistive (VR) constant-psi regimes
with parallel dynamics but without perpendicular resistivity
(classical transport). In the RI regime, the constant-psi equations
are second order; in the VR regime they are fourth order. We reproduce
known results in the RI regime, specifically real frequencies (the
Glasser effect), in spite of neglecting the classical transport (and
the divergence of the EXB drift). We find a Glasser effect in the VR
regime also, and show the connection between this effect and nearby
stable resistive interchanges. With no dissipation in the parallel
dynamics equations, i.e. the pressure and parallel velocity equations,
we observe a continuum due to the sound wave resonance.

In more recent work we have re-introduced perpendicular resistivity,
relaxed the constant-psi approximation, and formulated layer equations
in Fourier (k-) space. The full set of equations is fourth order in k
rather than 8th order in x. Inclusion of classical transport removes
the continuum, but introduces discrete modes. An important new factor
in the methodology is integration of the layer equations in terms of
the associated vector Riccati equation (VRE), which leads to third
order (nonlinear) equations in k-space. The motivation for using the
VRE is that it helps with the inherent stiffness in the layer
equations. The VRE results reproduce the constant-psi RI and VR regime
results discussed above (without the continuum) and show real
frequencies across a wide range of parameters.

[1] "Real frequency tearing layers with parallel dynamics and the
effect on locking and resistive wall modes", J. M. Finn, A. J. Cole,
and D. P. Brennan, arXiv: 1708.04700.