Kruskal–Shafranov instability criterion

E387066

The Kruskal–Shafranov instability criterion is a fundamental condition in plasma physics that predicts when a magnetically confined plasma column becomes unstable to kink-like distortions.

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Predicate Object
instanceOf magnetohydrodynamic instability criterion
plasma physics stability criterion
aimsToPrevent disruptive kink instabilities in fusion devices
appliesTo cylindrical plasma columns
magnetically confined plasma column
tokamak plasmas
z‑pinch configurations
assumes cylindrical symmetry approximation
ideal magnetohydrodynamics
category fusion energy physics concept
plasma stability theory
concerns current‑carrying plasmas
magnetohydrodynamic stability
coreCondition instability occurs when parallel current is too large relative to confining magnetic field
plasma column becomes kink‑unstable when twist of field lines exceeds about one turn over column length
safety factor q must exceed 1 for stability against m=1 kink mode in a tokamak
describes loss of axisymmetry due to kink deformation
transition from straight to helical plasma column shape
field magnetohydrodynamics
plasma physics
historicalPeriod mid‑20th century plasma physics
influenced development of tokamak safety factor design rules
stability limits in early pinch experiments
mathematicalForm L / (r B_z) < 2π / B_θ for stability of a cylindrical plasma column
q(a) > 1 for stability of m=1 kink in a simple tokamak model
modeType external kink mode
m=1 kink instability
namedAfter Martin David Kruskal
Vitaly Shafranov
predicts kink‑like distortions of plasma column
onset of kink instability
relatedConcept current‑driven instabilities
ideal MHD kink mode
magnetic shear
safety factor q profile
z‑pinch stability
relatesQuantity plasma column length
plasma column radius
plasma current
poloidal magnetic field
safety factor q
toroidal magnetic field
usedFor design of stable magnetic confinement devices
estimating maximum allowable plasma current
stability analysis of tokamak edge and core

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Martin David Kruskal notableWork Kruskal–Shafranov instability criterion
Kruskal knownFor Kruskal–Shafranov instability criterion
subject surface form: Martin David Kruskal
this entity surface form: Kruskal–Shafranov limit