Plasma Instability

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Plasma Instability
Types of instabilities MHD-Instabilities Resis
tive Instabilities Drift-instabilities
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Plasma Instabilities
Interchange instability Sausage instability Kink
instability
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Plasma StabilityIdeal MHD
Momentum Balance Ohms Law Continuity Adiabat
ic Law Amperes Law
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Plasma StabilityLinearisation
Neglect of quadratic terms
Result One equation for dV
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Energy Principle
The operator F is self-adjoint
Sufficient condition for stability
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Energy Principle
Stabilising term
Explicit form of the perturbed energy
Destabilising term
A currentless (homogeneous) plasma is stable
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Energy Principle
Destabilising term (Bernstein)
Torsion of field line
Normal to mag.surf.
Curvature of field line
Angle between k and n
Destabilising term (Greene)
Local shear
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Plasma Stability
Convex curvature (unstable)
Concave curvature(stable)
Plasma
Plasma
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Ballooning Mode Instability
Equation for marginal stability ---gt threshold
of pressure gradient
field line bending term
destabilizing term
Integrated local shear
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Normal Curvature W 7X
Torus inside view
Favourable curvature
Unfavourable curvature
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Summary
MHD-instabilities in Helias configurations have
been analysed numerically Interchange modes are
stabilised by a magnetic well Ballooning modes
are the most unstable modes The critical
averaged beta in Helias configurations is in the
range of 4 to 6