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Forces and torques within layers of driven tearing modes with sheared rotation

Author: Andrew J. Cole
Requested Type: Poster Only
Submitted: 2015-01-16 11:01:49

Co-authors: J. M. Finn, C. C. Hegna, P. W. Terry

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

Abstract Text:
For low amplitude tearing modes driven by error fields or coupling to other modes, in a
plasma with sheared rotation, the net force on a tearing layer due to Maxwell and Reynolds
stresses is calculated. The torque about the center of the tearing layer, also due to Maxwell
and Reynolds stresses, is also calculated. The force tends to cause the tearing layer to lock to
the phase of the driving perturbation, and the torque determines the evolution of the rotation
shear within the layer. These forces and torques are calculated for two constant-psi regimes of
tearing modes, namely the viscoresistive (VR) regime and the resistive-inertial (RI) regime,
and an ordering is shown in terms of the constant-psi small parameter e, the product of the tearing width and matching parameter. The velocity shear is taken to be first order in e. The
forces and torques are reported to the lowest order in e. The usual result for the Maxwell force
without rotation shear is recovered, i.e. the correction due to rotation shear is higher order, and
the lowest order contribution to the Reynolds force is zero. The Maxwell torque in the VR
regime is zero to lowest order. The Maxwell torque in the RI regime is small (e^5/2) and
proportional to the rotation shear within the layer. The treatment of the tearing layers is by
means of variational principles using Padé approximants[1]. The Reynolds torque is zero for
the VR regime. For the RI regime it is O(e^3/2) and is proportional to the rotation shear across
the layer. The Reynolds torque is analogous to the effect that can drive zonal flows in other
contexts. These results are applied to the multimode case, in which many modes are driven
and their tearing layers overlap.
[1] A. J. Cole and J. M. Finn, “Variational principles with Padé approximants for tearing
mode analysis”, Phys. Plasmas 21, 032508 (2014).

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