In relativistic laser-plasma physics the relativistic similarity parameter S is a dimensionless parameter defined as where
is the electron plasma density,
is the critical plasma density and
is the normalized vector potential.
the electric vacuum permittivity and
is the laser frequency.
were first introduced in plasma physics by Sergey Gordienko.
[1] It allows distinguishing between relativistically overdense
and underdense plasmas
The similarity parameter is connected to basic symmetry properties of the collisionless Vlasov equation and is thus the relativistic plasma analog of the Reynolds number in fluid mechanics.
Gordienko showed that in the relativistic limit (
) the laser-plasma dynamics depends on three dimensionless parameters:
is the duration of the laser pulse and
is the typical radius of the laser waist.
The main result of the relativistic similarity theory can be summarized as follows: if the parameters of the interaction (plasma density and laser amplitude) change simultaneously so that the
parameter remains constant, the dynamics of the electrons remains the same.
The similarity theory allows deriving non-trivial power-law scalings for the energy of fast electrons in underdense and overdense plasmas.
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