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δ function in 4D phase space; see Ref. [2]
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A Kronecker δ function in 4D phase space; see Ref. [2].
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Kronecker, A.1
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20
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0342672962
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A Heaviside step function in 4D space
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A Heaviside step function in 4D space.
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21
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0343979108
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note
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From a thermodynamic perspective the natural equilibrium state is the Maxwell-Boltzmann (MB), i.e., thermal distribution with self-consistent inclusion of the space-charge fields [2]. Note that a MB distribution with two temperatures is not in general a stationary solution of the Vlasov equation (see, for instance, [7]).
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0343543160
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edited by A. U. Luccio and William W. MacKay IEEE, Piscataway, NJ
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2 is the space charge intensity parameter defined by M. Reiser et al., in Proceedings of the 18th Particle Accelerator Conference, 1999, New York City, edited by A. U. Luccio and William W. MacKay (IEEE, Piscataway, NJ, 1999), p. 234.
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