In relativistic laser-plasma physics the relativistic similarity parameter ''S'' is a
dimensionless parameter
A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no Dimension (physics), physical dimension is assigned, with a corresponding International Sys ...
defined as
:
,
where
is the electron plasma density,
is the critical plasma density and
is the normalized vector potential. Here
is the
electron mass
The electron mass (symbol: ''m''e) is the mass of a stationary electron, also known as the invariant mass of the electron. It is one of the fundamental constants of physics. It has a value of about or about , which has an energy-equivalent of a ...
,
is the electron charge,
is the speed of light and
is the laser frequency. Note that
CGS units were used above.
The concept of similarity and the similarity parameter
were first introduced in plasma physics by Sergey Gordienko. It allows distinguishing between relativistically overdense
and underdense plasmas
.
The similarity parameter is connected to basic symmetry properties of the collisionless
Vlasov equation The Vlasov equation is a differential equation describing time evolution of the Distribution function (physics), distribution function of plasma (physics), plasma consisting of charged particles with long-range interaction, e.g. Coulomb's law, Coulo ...
and is thus the
relativistic plasma Relativistic plasmas in physics are plasmas for which relativistic corrections to a particle's mass and velocity are important. Such corrections typically become important when a significant number of electrons reach speeds greater than 0.86 c (Lo ...
analog of the
Reynolds number
In fluid mechanics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces. At low Reynolds numbers, flows tend to be domi ...
in
fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and bio ...
. Gordienko showed that in the relativistic limit (
) the laser-plasma dynamics depends on three dimensionless parameters:
,
and
, where
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.
References
Plasma physics
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