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Thus, the usual procedure involves the calculation of the electric and magnetic fields due to all the particles and then the calculation of the motion of the plasma particles under the forces arising from these internal fields as well as external fields. This treatment is valid for interactions among particles which take place at distances greater than the Debye length. However, a small number of interactions take place at distances shorter than a Debye length. These latter, close-range interactions are treated as two-body “scattering” events.

13. Calculate the curvature drift speed for protons and electrons in plasma at 10 keV with B ¼ 5 T and a field radius of curvature R ¼ 10 m. 14. Derive an expression for the drift velocity due to gravity. 1 Equilibrium and Pressure Balance The basic equations which determine the plasma equilibrium are the momentum balance equation relating the force due to the pressure gradient to the Lorentz force acting on all of the particles in a unit volume of plasma. 0 ¼ Àrp þ j  B and Ampere’s law m0 j ¼ rÂB From the first equation, jÁrp ¼ 0 and BÁrp ¼ 0.

Mvth ¼ ’ jVj jejB jejB where the thermal velocity is vth ¼ For ions (i) and electrons (e), pffiffiffiffiffiffiffiffiffiffiffiffi 2T=m. Ve ¼ À1:76 Â 1011 BðTÞ rad=sec Vi ¼ 0:96 Â 108 BðTÞ rad=sec with B in Tesla and rLe ¼ 1:066 Â 10À4 rLi ¼ 4:57 Â 10À3 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi À Áffi Te keV BðTÞ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi À Á Ai Ti keV zi BðTÞ m m where Ai and zi are atomic mass (amu) and atomic number. 8 Drifts When an electric field is present or when the magnetic field is nonuniform, the motion is more complicated because the form of the force term in the equation of motion is more complex.