[Paper Review] Introduction to Plasma Accelerators: the Basics

R. Bingham, R. M. G. M. Trines|Strathprints: The University of Strathclyde institutional repository (University of Strathclyde)|Feb 10, 2016

Laser-Plasma Interactions and Diagnostics3 citations

TL;DR

This paper provides a foundational overview of plasma wakefield accelerators, explaining how intense lasers or electron beams excite relativistic plasma waves in low-density plasmas to achieve accelerating gradients up to 1,000 times higher than conventional RF accelerators. It derives the core equations governing laser-driven wakefield excitation using relativistic fluid dynamics and Maxwell’s equations, demonstrating how these waves can accelerate electrons and even photons in the blowout regime.

ABSTRACT

In this article, we concentrate on the basic physics of relativistic plasma wave accelerators. The generation of relativistic plasma waves by intense lasers or electron beams in low-density plasmas is important in the quest for producing ultra-high acceleration gradients for accelerators. A number of methods are being pursued vigorously to achieve ultra-high acceleration gradients using various plasma wave drivers; these include wakefield accelerators driven by photon, electron, and ion beams. We describe the basic equations and show how intense beams can generate a large-amplitude relativistic plasma wave capable of accelerating particles to high energies. We also demonstrate how these same relativistic electron waves can accelerate photons in plasmas.

Motivation & Objective

• To establish the theoretical basis for plasma wakefield acceleration as a compact alternative to conventional particle accelerators.
• To explain how intense laser or electron beams excite large-amplitude relativistic plasma waves in low-density plasmas.
• To derive and analyze the governing equations for laser wakefield excitation using relativistic hydrodynamics and the quasi-static approximation.
• To demonstrate the potential for ultra-high accelerating gradients—up to ~10^9 V/cm—enabling table-top accelerators.
• To explore the possibility of photon acceleration via relativistic plasma waves, extending the applicability of plasma-based acceleration.

Proposed method

• Uses one-fluid, cold relativistic hydrodynamics to model electron dynamics under intense laser or beam fields.
• Applies Maxwell’s equations with a vector potential envelope approximation to describe the electromagnetic drive pulse.
• Employs the quasi-static approximation to neglect time derivatives in electron fluid equations, simplifying the system to steady-state-like dynamics.
• Derives coupled nonlinear equations for the laser vector potential envelope, plasma density, and electrostatic potential.
• Introduces the blowout or bubble regime where laser pulse length is comparable to the plasma wavelength, leading to a single-period, ion-column-driven wakefield.
• Solves the wave equation for the vector potential under the envelope approximation, linking it to plasma density and relativistic gamma factors.

Experimental results

Research questions

• RQ1 How do intense laser pulses excite large-amplitude relativistic plasma waves in low-density plasmas?
• RQ2 What are the fundamental equations governing the self-consistent evolution of laser wakefields in the relativistic, quasi-static regime?
• RQ3 How do accelerating gradients in plasma wakefield accelerators exceed those in conventional RF cavities?
• RQ4 In what way can relativistic plasma waves also accelerate photons, and what are the conditions for this process?
• RQ5 What physical mechanisms lead to the formation of the bubble or blowout regime in laser-plasma interactions?

Key findings

• Plasma wakefield accelerators can support accelerating fields of approximately 10^9 V/cm, which is about 1,000 times higher than conventional RF accelerators.
• The accelerating field scales with the square root of electron density, E ∝ n^{1/2}, enabling high gradients in high-density plasmas.
• In the blowout regime, the laser pulse creates a cavity-like structure with a trailing ion column that drives a strong, single-period wakefield.
• The maximum wakefield amplitude is reached within the laser pulse, and the time to reach this amplitude is on the order of the laser pulse duration.
• Relativistic plasma waves can accelerate both electrons and photons, extending the scope of plasma-based acceleration beyond charged particles.
• The model equations derived using the quasi-static approximation and envelope method accurately describe the formation and evolution of the wakefield in the relativistic regime.