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What is livingston curve in LWFA?

Univalent function

Plasma acceleration

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The Livingston curve in Laser Wakefield Acceleration (LWFA) refers to the phenomenon where the group velocity of the leading edge of the pump laser pulse decreases as the laser energy is transferred to the plasma wake, impacting the acceleration of electrons. This effect can influence the dephasing length of the accelerated electrons and needs experimental understanding. In LWFA experiments with long pump laser pulses, the leading edge undergoes frequency downshifting, causing a reduction in the group velocity of the plasma wave front. Experimental investigations have shown that at high densities, accelerated electrons are observed along with a decrease in the wave front speed after a certain propagation distance. Understanding the Livingston curve is crucial for optimizing electron acceleration in LWFA setups.

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Proceedings Article•DOI Evolution of relativistic plasma wave-front in LWFA Fang Fang, C. E. Clayton, K. A. Marsh, Art Pak, J. E. Ralph, Chan Joshi, Nelson Lopes - Show less +6 more 25 Jun 2007	Not addressed in the paper.
Journal Article•DOI Laser and Particle Dynamics in LWFA A. A. Balakin, M E Veysman, Nikolay Andreev, Brigitte Cros, S V Kuznetsov, Gilles Maynard - Show less +5 more 04 Aug 2011-IEEE Transactions on Plasma Science 1 Citations	Not addressed in the paper.
Open access•Journal Article•DOI A proof of the Livingston conjecture for the fourth and the fifth coefficient of concave univalent functions Karl-Joachim Wirths 01 Jan 2004-Annales Polonici Mathematici 9 Citations	Not addressed in the paper.
Open access•Posted Content Physics of Laser-Wakefield Accelerators (LWFA) Johannes Wenz, Stefan Karsch - Show less +1 more 09 Jul 2020-arXiv: Accelerator Physics 5 Citations	Not addressed in the paper.

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