Power-Law Scaling Relating the Average Charge State and Kinetic Energy in Expanding Laser-Driven Plasmas

A universal power-law scaling <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mover accent="true"><a:mrow><a:mi>z</a:mi></a:mrow><a:mrow><a:mo stretchy="false">¯</a:mo></a:mrow></a:mover><a:mo>∝</a:mo><a:msup><a:mrow><a:mi>E</a:mi></a:mrow><a:mrow><a:mn>0.4</a:mn></a:mrow></a:msup></a:mrow></a:math> in the correlation between the average ion charge state <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mover accent="true"><e:mi>z</e:mi><e:mo stretchy="false">¯</e:mo></e:mover></e:math> and kinetic energy <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>E</i:mi></i:math> in expanding laser-driven tin plasmas is identified. Universality here refers to an insensitivity to all experimental conditions: target geometry, expansion direction, laser wavelength, and power density. The power law is accurately captured in an analytical consideration of the dependence of the charge state on temperature and the subsequent transfer of internal to kinetic energy in the expansion. These analytical steps are individually, and collectively, validated by a two-dimensional radiation-hydrodynamic simulation of an expanding laser-driven plasma. This power-law behavior is expected to hold also for dense plasma containing heavier, complex ions such as those relevant to current and future laser-driven plasma light sources.