Relativistic similarity parameter
Encyclopedia
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. Here 
is the electron mass, 
is the electron charge, 
is the speed of light and the laser 
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
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: 
, 
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 similar.
The similarity theory allows deriving non-trivial power-law scalings for the energy of fast electrons in underdense and overdense plasmas.
,where
is the electron plasma density, is the critical plasma density and is the normalized vector potential. Here is the electron mass, is the electron charge, is the speed of light and the laser 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
Vlasov equation
The Vlasov equation is a differential equation describing time evolution of the distribution function of plasma consisting of charged particles with long-range interaction...
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: , 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 similar.The similarity theory allows deriving non-trivial power-law scalings for the energy of fast electrons in underdense and overdense plasmas.