Collisional relaxation of a strongly magnetized two-species pure ion plasma
- Department of Physics, University of California at San Diego, La Jolla, California 92093 (United States)
The collisional relaxation of a strongly magnetized pure ion plasma that is composed of two species with slightly different masses is discussed. We have in mind two isotopes of the same singly ionized atom. Parameters are assumed to be ordered as Ω{sub 1},Ω{sub 2}≫|Ω{sub 1}−Ω{sub 2}|≫v{sup ¯}{sub ij}/b{sup ¯} and v{sup ¯}{sub ⊥j}/Ω{sub j}≪b{sup ¯}, where Ω{sub 1} and Ω{sub 2} are two cyclotron frequencies, v{sup ¯}{sub ij}=√(T{sub ∥}/μ{sub ij}) is the relative parallel thermal velocity characterizing collisions between particles of species i and j, and b{sup ¯}=2e{sup 2}/T{sub ∥} is the classical distance of closest approach for such collisions, and v{sup ¯}{sub ⊥j}/Ω{sub j}=√(2T{sub ⊥j}/m{sub j})/Ω{sub j} is the characteristic cyclotron radius for particles of species j. Here, μ{sub ij} is the reduced mass for the two particles, and T{sub ∥} and T{sub ⊥j} are temperatures that characterize velocity components parallel and perpendicular to the magnetic field. For this ordering, the total cyclotron action for the two species, I{sub 1}=∑{sub i∈1}m{sub 1}v{sub ⊥i}{sup 2}/(2Ω{sub 1}) and I{sub 2}=∑{sub i∈2}m{sub 2}v{sub ⊥i}{sup 2}/(2Ω{sub 2}) are adiabatic invariants that constrain the collisional dynamics. On the timescale of a few collisions, entropy is maximized subject to the constancy of the total Hamiltonian H and the two actions I{sub 1} and I{sub 2}, yielding a modified Gibbs distribution of the form exp[−H/T{sub ∥}−α{sub 1}I{sub 1}−α{sub 2}I{sub 2}]. Here, the α{sub j}’s are related to T{sub ∥} and T{sub ⊥j} through T{sub ⊥j}=(1/T{sub ∥}+α{sub j}/Ω{sub j}){sup −1}. Collisional relaxation to the usual Gibbs distribution, exp[−H/T{sub ∥}], takes place on two timescales. On a timescale longer than the collisional timescale by a factor of (b{sup ¯2}Ω{sub 1}{sup 2}/v{sup ¯}{sub 11}{sup 2})exp(5[3π(b{sup ¯}|Ω{sub 1}−Ω{sub 2}|/v{sup ¯}{sub 12})]{sup 2/5}/6), the two species share action so that α{sub 1} and α{sub 2} relax to a common value α. On an even longer timescale, longer than the collisional timescale by a factor of the order exp(5[3π(b{sup ¯}Ω{sub 1}/v{sup ¯}{sub 11})]{sup 2/5}/6), the total action ceases to be a good constant of the motion and α relaxes to zero.
- OSTI ID:
- 22253118
- Journal Information:
- Physics of Plasmas, Vol. 21, Issue 4; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 1070-664X
- Country of Publication:
- United States
- Language:
- English
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