biMaxwellian

BiMaxwellian is a term used in plasma physics to describe a velocity distribution of particles in a magnetized plasma where the distribution is Maxwellian in both directions, but with different temperatures parallel and perpendicular to the magnetic field. This anisotropy reflects different heating or cooling processes along and across magnetic field lines and is common in magnetized environments such as the solar wind, planetary magnetospheres, and tokamak edge plasmas.

The BiMaxwellian distribution function, oriented with the magnetic field along the z-axis, can be written as

f(v) = n / (π^(3/2) v_th_perp^2 v_th_para) × exp[-(v_x^2 + v_y^2)/v_th_perp^2 - v_z^2/v_th_para^2],

where v_perp^2 = v_x^2 + v_y^2, v_para = v_z, and v_th_perp = sqrt(2 k_B T_perp / m), v_th_para = sqrt(2 k_B T_para / m). Here n is the number density, T_perp is the temperature perpendicular to B, and T_para is the temperature parallel to B.

Physically, the BiMaxwellian implies a pressure tensor with P_perp = n k_B T_perp and P_para = n k_B T_para, while off-diagonal elements vanish in the chosen frame. If T_perp equals T_para, the distribution reduces to the ordinary isotropic Maxwellian. Anisotropy (T_perp ≠ T_para) can drive kinetic and magnetohydrodynamic instabilities, such as mirror or firehose modes, depending on the plasma beta and the degree of anisotropy.

Applications include modeling and fitting observed particle distributions in space plasmas, informing kinetic theory and Vlasov simulations, and providing a tractable model for anisotropic heating scenarios in fusion devices.