Wakefield generation and GeV acceleration in tapered plasma channels

Abstract

To achieve multi-GeV electron energies in the laser wakefield accelerator (LWFA), it is necessary to propagate an intense laser pulse long distances in a plasma without disruption. One of the purposes of this paper is to evaluate the stability properties of intense laser pulses propagating extended distances (many tens of Rayleigh ranges) in plasma channels. A three-dimensional envelope equation for the laser field is derived that includes nonparaxial effects such as group velocity dispersion, as well as wakefield and relativistic nonlinearities. It is shown that in the broad beam, short pulse limit the nonlinear terms in the wave equation that lead to Raman and modulation instabilities cancel. This cancellation can result in pulse propagation over extended distances, limited only by dispersion. Since relativistic focusing is not effective for short pulses, the plasma channel provides the guiding necessary for long distance propagation. Long pulses (greater than several plasma wavelengths), on the other hand, experience substantial modification due to Raman and modulation instabilities. For both short and long pulses the seed for instability growth is inherently determined by the pulse shape and not by background noise. These results would indicate that the self-modulated LWFA is not the optimal configuration for achieving high energies. The standard LWFA, although having smaller accelerating fields, can provide acceleration for longer distances. It is shown that by increasing the plasma density as a function of distance, the phase velocity of the accelerating field behind the laser pulse can be made equal to the speed of light. Thus electron dephasing in the accelerating wakefield can be avoided and energy gain increased by spatially tapering the plasma channel. Depending on the tapering gradient, this luminous wakefield phase velocity is obtained several plasma wavelengths behind the laser pulse. Simulations of laser pulses propagating in a tapered plasma channel are presented. Experimental techniques for generating a tapered density in a capillary discharge are described and an example of a GeV channel guided standard LWFA is presented.

Laser guiding for GeV laser–plasma accelerators

“…Much higher net energy gains can be realized for the same amount of input laser power by extending the acceleration distance beyond Z R . Guiding concepts relying on the use of preformed channels are being studied by several groups around the world (Volfbeyn et al 1999;Geddes et al 2004a;Alexeev et al 2003;Downer et al 2003;Tochitsky et al 2004;Sprangle et al 2001;Spence & Hooker 2001;Zhidkov et al 2004;Lopes et al 2003;Chen et al 2004;Cros et al 2002). At LBNL, using the ignitor-heater concept (Volfbeyn et al 1999), we have recently produced plasma channels that have guided, to our knowledge, the highest peak power and the highest intensity in a preformed channel (Geddes et al 2004a).…”

Comment on “Self-focusing and channel-coupling effects on short laser pulses propagating in a plasma channel” [Phys. Plasmas 11, 3259 (2004)]

“…2 However, in the presence of a nonlinear source, this method puts too much emphasis on the central part of the beam and is known to give a large error in the value of the threshold power for self-focusing. In the following, for comparison, we analyze the wave equation ͑2͒ by means of the source-dependent expansion ͑SDE͒ method [3][4][5][6][7][8][9] so that one can identify the effect of channel coupling on the pulse-focusing properties.…”

“…Although nonparaxial propagation of a short laser pulse in a plasma channel, i.e., in the presence of finite pulse length effects, has been studied in detail by Esarey and Leemans, 2 Esarey et al, 3 and Sprangle et al [4][5][6][7][8] in the linear as well as in the nonlinear case with the relativistic nonlinearity, Jha et al 1 expect that for a moderately relativistic intense laser pulse the channel-coupling effect will alter the pulse-focusing properties significantly, and they demonstrate this by means of the heuristic method.…”

“…denotes the complex conjugate. Using Coulomb gauge ٌ · a = 0, in the presence of relativistic and channel-coupling nonlinearities, the wave equation for the laser field is given by [1][2][3][4][5][6][7][8][9] …”

Advances in Laser Driven Accelerator R&D

“…Guiding concepts relying on the use of preformed channels are being studied by several groups around the world, including LBNL [15,12], University of Maryland [16], University of Texas at Austin [17], UCLA [18], Naval Research Laboratory [19], Oxford University-UK [20], Japan [21], IST Lisbon-Portugal [22], Taiwan [23] and France [24]. At LBNL, using the ignitor-heater concept [15], we have recently produced plasma channels that have guided, to our knowledge, the highest peak power in a preformed channel [12].…”