An equilibrium and stability problems of a plasma in lieliotron magnetic field are discussed under the assumption that the plasma behaves such as hydromagnetic fluid and its pressure is much less than a magnetic pressure.
When the plasma carries only a diamagnetic J
θ current and not a j
z current due to a external electric field, for instance, joule heating electric field, the plasma quantities satisfying the equilibrium conditions take some reasonable distribution.
Both equilibrium plasma pressure and diamagnetic current can be expressed respectively in the forms.
P=α
0ψ
0/n (1-ψ/ψ
0)
nj
θ=-α
0r (1-ψ/ψ
0)
n-1where φ=rA
θThe stability condition for the flute type instability is given as follows;γpB
2∂/∂ψ (1/B
2) +∂p/∂ψ>0.
The equilibrium state satisfying the above condition takes the next inequality;γ/n>1.51
where γ is the ratio of the specific heats.
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