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Plasma Theory at PBPL

Historical Overview and Significant Publications

Plasma physics at PBPL was heralded by theoretical and experimental work carried out by Prof. Rosenzweig prior to his arrived at UCLA. He published a seminal work on the nonlinear, relativistic one-dimensional theory of plasma wake-field acceleration (PWFA): "Nonlinear Plasma Dynamics in the Plasma Wake-Field Accelerator", J.B. Rosenzweig, Phys. Rev. Lett. 58, 555 (1987). In this work, the theory of PWFA was extended to nonlinear systems, and such issues as density spiking, sawtooth acceleration field, excitation efficiency, and transformer ratio were examined using an exact 1D analysis based on the methods of Ahkiezer and Polovin. This was followed by a series of investigations into the 1D theory of the PWFA: notably, wave-breaking effects "Trapping, Thermal Effects and Wave Breaking in the Nonlinear Plasma Wake-field Accelerator'', J.B. Rosenzweig, Phys. Rev. A 38, 3634 (1988) ;

and multiple fluid models for describing low energy electron beams as well as ion motion, "Multi-Fluid Models for Plasma Wake-field Phenomena'' J. B. Rosenzweig, Phys. Rev. A 40, 5249 (1989). This work was carried out at roughly the same time as investigations into plasma lensing, and its application to the final focus of a linear collider, was ongoing. Studies began in the overdense (beam less dense than the plasma, with linear plasma response) "Beam Optics of a Self-focusing Plasma Lens", J.B. Rosenzweig and P. Chen, Phys. Rev. D 39, 2039 (1989) ; and proceeded to studies of the underdense regime, where the beam is much denser than the plasma. In the underdense regime focusing of the plasma ions provides high quality, linear focusing fields "Final Focusing and Enhanced Disruption from an Underdense Plasma Lens in a Linear Collider", P. Chen, S. Rajagopalan, and J. Rosenzweig, Phys. Rev. D 40, 923 (1989).

After arriving at UCLA, Prof. Rosenzweig produced one of the most significant theoretical discoveries in the PWFA field, that of the "blow-out" regime. This regime can be understood as a combination of the underdense plasma lens (the beam's space-charge repels essentially all of the plasma electrons from the beam channel), and the nonlinear PWFA (the beam is short, and leaves a strong wake-field after its passage). It was pointed out that the combination of high quality focusing fields, and acceleration that is independent of transverse position was qualitatively different than the linear regime of the PWFA; one could consider preserving the transverse and longitudinal emittances of the beam just as in a linac. This investigation was based on numerical solution of the two-dimensional (cylindrical symmetry, r-z) fluid equations as proposed by Breizman, and on 2D particle-in-cell simulations. It is contained in "Acceleration and Focusing of Electrons in Two-Dimensional Nonlinear Plasma Wake-fields'', J. B. Rosenzweig, et al., Phys. Rev. A -- Rapid Comm . 44, R6189 (1991).

Figure 1: Longitudinal electric field in nonlinear PWFA, from PIC simulation, showing saw-tooth like field profile in z.

Figure 2: Wakefields as a function of radial offset r inside of plasma electron-rarefied region, showing linear focusing fields, and acceleration fields independent of r.

This was a truly seminal paper, as it can be noted that essentially all present experiments in PWFA are performed in the blow-out regime. While nonlinear plasma wakes had already been observed at the point of publication ("Experimental Measurement of Nonlinear Plasma Wake-fields", J. B. Rosenzweig, et al., Phys. Rev. A - Rapid Comm. 39, 1586 (1989).), the beam properties needed for accessing the blow-out regime were not achieved for roughly ten years after this paper was published. As a component of the work on UCLA PBPL/ANL nonlinear PWFA experiment, a study of the self-consistent beam characteristics needed for transverse beam stability in the blow-out regime was published by the PBPL, "Propagation of Short Electron Pulses in an Underdense Plasma", N. Barov and J.B. Rosenzweig, Phys. Rev. E 49 4407 (1994).

Theoretical work on the PWFA at PBPL took a backseat to experimental studies over the following years. As an outgrowth of the experimental studies, however, a series of papers on the "straw-man" design of a PWFA-based, modular approach to linear collider were produced: "Towards a Plasma Wake-field Acceleration-based Linear Collider", J.B. Rosenzweig, et al., Nuclear Instruments and Methods A 410 532 (1998).

Figure 3. Schematic picture of a modular plasma wake-field accelerator-based collider (g-g option) driven from a single heavily beam-loaded injector complex.

The PBPL hiatus on theoretical PWFA investigations ended in 2001 with the paper which introduced the exciting proposal that by using a density transition, one may trap a self-phase-locked beam of electrons from the background plasma:"Plasma Electron Trapping and Acceleration in a Plasma Wake Field Using a Density Transition", H. Suk, N. Barov, J. B. Rosenzweig, and E. Esarey, Phys. Rev. Lett. 86, 1011 (2001).

The physical mechanism for the trapping of background electrons near a density transition was clarified in a one-dimensional study utilizing a Lagrangian analysis: "Plasma electron fluid motion and wave breaking near a density transition", R. J. England, J. B. Rosenzweig, and N. Barov Phys. Rev. E 66, 016501 (2002).

The transition trapping proposal has led to studies of the on-going proof-of-principle experiment undertaken at the FNAL A0 photoinjector by a UCLA PBPL/NICADD collaboration. This PIC simulation study shows that by properly tailoring the plasma density profile, and scaling to high plasma density, a transition-trapping source may achieve higher brightness than existing photoinjector sources: "Plasma density transition trapping as a possible high-brightness electron beam source", M. C. Thompson, J. B. Rosenzweig, and H. Suk, Phys. Rev. ST Accel. Beams 7, 011301 (2004).

Figure 4. PIC simulation of the process of trapping plasma electrons at a strong downward density transition, showing progressively later times, with beam (not shown) moving to the right. Electrons initially downstream of the transition are blue, initially upstream are red; the trapped electrons come mainly from initial upstream positions.

Figure 5. Simulated longitudinal phase space of PBPL/NICADD transition trapping experiment, showing narrow energy spread trapped beam, achieved by tailoring plasma density downward after transition.

In the past several years, it has been appreciated by all groups involved in PWFA experimental work that in order to optimally excite plasma wake-fields, the plasma density should be raised, while keeping the relation . This relation produces fields that scale as the familiar Cerenkov energy loss, . Thus present experiments are concerned with using very short beams to achieve high acceleration gradients. Recent work at NICADD (Barov) and PBPL has examined the validity of this scaling using an exact analysis of the energy loss of an infinitesimally short beam. It was found that, due to an as yet undiscovered effect, the strong "snow-plowing" of plasma electrons which gives rise to a very short-lived high density spike, the energy loss scales linearly with the charge , even for extremely large normalized charge (the ratio of the beam electrons to plasma electrons located in the relevant volume, a cubic plasma skin-depth).

The above analysis is contained in the paper: "Energy Loss of a High Charge Bunched Electron Beam in Plasma: Analysis" N. Barov, J.B. Rosenzweig, M.C. Thompson, and R.B. Yoder, submitted to Physical Review Special Topics – Accelerators and Beams; also in The Physics and Applications of High Brightness Electron Beams, Ed. J. Rosenzweig, G. Travish and L. Serafini (World Scientific, 2003).

Figure 6. The snow-plowing of plasma electrons by an ultra-short beam, very high charge beam (located near r <0.005 m, z=0.0185 m), as illustrated by the density (false color map: low-violet, high-red). Note that first the plasma electrons snow-plow to ten times ambient density in the region of the beam due to longitudinal velocity, and then move outward to rarefy the beam channel (blow-out). In this simulation the normalized charge

The ultra-short beam limit allows one to analyze the new physics of snow-plow, which led to the anomalous behavior of linear-like energy loss. It is of course of further interest to look at finite length beams, their scaling of energy loss, and of the accelerating fields left in the beam's wake. These issues have been explored using PIC simulations in the following paper: "Energy Loss of a High Charge Bunched Electron Beam in Plasma: Simulations, Scaling, and Accelerating Wake-fields" J.B. Rosenzweig, N. Barov, M.C. Thompson, and R.B. Yoder, submitted to Physical Review Special Topics – Accelerators and Beams; also in The Physics and Applications of High Brightness Electron Beams, Ed. J. Rosenzweig, G. Travish and L. Serafini (World Scientific, 2003).

The above paper concludes that for , or so, that linear-like scaling of beam energy loss, and acceleration fields in the blow-out regime of the PWFA is violated.

Figure 7. The average normalized energy loss rate of of a Gaussian-current electron beam with length , width , as a function of , from linear theory (solid bold line) and self-consistent PIC simulation (circles); the peak accelerating field behind the beam, , from linear theory (solid fine line) and PIC simulation (squares); also the useful field for acceleration (diamonds).