Plasma dynamics in transient electrostatic shocks driven by relativistic few-cycle laser pulses

The rapid advancement of laser compression techniques has brought increasing attention to few-cycle laser-plasma interactions. Through comprehensive particle-in-cell simulations, we demonstrate that compressing laser pulses to sub-10-femtosecond durations significantly enhances transient electrostatic shocks. Crucially, the plasma dynamics are strongly modulated by the laser carrier-envelope phase ( <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mrow> <a:msub> <a:mrow> <a:mi mathvariant="normal">Φ</a:mi> </a:mrow> <a:mrow> <a:mtext>CEP</a:mtext> </a:mrow> </a:msub> </a:mrow> </a:math> ). Our results reveal a pronounced cosinelike dependence of the proton cutoff energy on <d:math xmlns:d="http://www.w3.org/1998/Math/MathML" display="inline"> <d:mrow> <d:msub> <d:mrow> <d:mi mathvariant="normal">Φ</d:mi> </d:mrow> <d:mrow> <d:mtext>CEP</d:mtext> </d:mrow> </d:msub> </d:mrow> </d:math> , with certain values of <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"> <g:mrow> <g:msub> <g:mrow> <g:mi mathvariant="normal">Φ</g:mi> </g:mrow> <g:mrow> <g:mtext>CEP</g:mtext> </g:mrow> </g:msub> </g:mrow> </g:math> yielding superior performance due to enhanced electron displacement and stronger charge-separation fields. Phase-space analysis uncovers expanding “source”-like electron orbits, whose gyration radii correlate with <j:math xmlns:j="http://www.w3.org/1998/Math/MathML" display="inline"> <j:mrow> <j:msub> <j:mrow> <j:mi mathvariant="normal">Φ</j:mi> </j:mrow> <j:mrow> <j:mtext>CEP</j:mtext> </j:mrow> </j:msub> </j:mrow> </j:math> -dependent energy transfer. We further develop an analytical model connecting the electrostatic shock strength, inferred from the proton energy, to the laser-plasma interaction parameters. This model is validated through extensive parameter scans over target density, thickness, laser intensity, and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"> <m:mrow> <m:msub> <m:mrow> <m:mi mathvariant="normal">Φ</m:mi> </m:mrow> <m:mrow> <m:mtext>CEP</m:mtext> </m:mrow> </m:msub> </m:mrow> </m:math> . Our findings establish a predictive framework for <p:math xmlns:p="http://www.w3.org/1998/Math/MathML" display="inline"> <p:mrow> <p:msub> <p:mrow> <p:mi mathvariant="normal">Φ</p:mi> </p:mrow> <p:mrow> <p:mtext>CEP</p:mtext> </p:mrow> </p:msub> </p:mrow> </p:math> -controlled plasma dynamics in short-pulse laser interactions, providing insight into mechanisms relevant to laboratory high-energy proton sources and origin of energetic cosmic rays in astrophysical environments.