Pressure Plasma Equilibrium in Magnetic Field and Pinch Effect

Magnetic Pressure Plasma Equilibrium in Magnetic Field and Pinch Effect 

In steady-state conditions dvjdt = 0), the Navier-Stokes equation (3-251) can be simplified to 

This equation can be interpreted as a balance of hydrostatic pressure p and Ampere force exerted on the plasma. Taking into account the first of equations (3-253), the current can be eliminated from the balance  

Combination of the gradients leads to the equation for plasma equilibrium in the magnetic field  

The equation (3-259) for plasma equilibrium in a magnetic field can be considered a dynamic balance of the gradient of total pressure and the tension of magnetic lines. If the magnetic field lines are straight and parallel, then R oo and the tension of magnetic lines is eqnal to zero. In this case, equation (3-259) gives the equilibrinm criterion  

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