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Relativistic Vlasov-Maxwell System

The relativistic Vlasov-Maxwell system couples the phase-space density of charged particles to their electromagnetic fields. In a one-species normalization on R_x^3×R_p^3, put v(p)=p/sqrt(1+||p||^2). The equations are

partial_tf+v·del _xf+(E+v×B)·del _pf=0,
(1)
partial_tE-del ×B=-j
(2)
partial_tB+del ×E=0,
(3)
del ·E=rho
(4)
del ·B=0,
(5)

where rho=intfdp and j=intv(p)fdp. There is no background charge in this convention.

See also

Maxwell's Equations, Partial Differential Equation, Phase Space

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References

Luk, J. and Strain, R. M. "A New Continuation Criterion for the Relativistic Vlasov-Maxwell System." Commun. Math. Phys. 331, 1005-1027, 2014. https://doi.org/10.1007/s00220-014-2108-8.

Cite this as:

Weisstein, Eric W. "Relativistic Vlasov-Maxwell System." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/RelativisticVlasov-MaxwellSystem.html

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