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Formation of electrostatic structures by wakefield acceleration in ultrarelativistic plasma flows: Electron acceleration to cosmic ray energies
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View: Figures


Image of FIG. 1.
FIG. 1.

The simulation model. The collapse of a star is associated with the ejection of a plasma jet into the ambient medium, e.g., in the interstellar medium or the stellar wind of the progenitor star, and an external shock forms at its leading edge. Plasma velocity gradients within the jet result in internal shocks. In the inset the internal shock moves upward into the foreshock region, where it reflects protons (dashed lines). The simulation box is at rest in the foreshock.

Image of FIG. 2.
FIG. 2.

The initial plasma phase space distribution. The (upstream) background electrons and protons initially have a mean speed of zero. The shock-reflected protons constitute beam 1. Beam 2 does not participate significantly in the plasma dynamics. It provides a current that compensates that of the beam 1. The simulation boundaries are periodic and the particles are wrapped around, as indicated by the arrows.

Image of FIG. 3.
FIG. 3.

(Color online) The wave evolution. The spectrum of the electrostatic waves . The wave numbers are normalized to the most unstable of the two-stream instability, and the time is normalized to . The color scale shows the 10-logarithmic normalized amplitude modulus. The white line shows .

Image of FIG. 4.
FIG. 4.

(Color online) Particle distribution functions. (a) Electron phase space distribution for a subsection of the simulation box at the time . (b) Exhibits the phase space distribution of the proton beam for the same box interval and time. The color scales show the particle phase-space number densities in a 10-logarithmic scale.

Image of FIG. 5.
FIG. 5.

The wakefield accelerator. (a) Mean speed of the proton beam, as a function of the position. (b) Electron number density , that has been integrated over the velocity range . The square root of has been taken to better resolve its dynamical range. The proton mean speed decreases to larger negative speeds at the cell 4550, which coincides with the peak electron density. The proton mean speed further shows a change in the slope at cell 4600, which corresponds to a change in the slope of the electron density at the same cell. The proton mean speed modulus has its maximum at cell 4700 where drops to 0.

Image of FIG. 6.
FIG. 6.

(Color online) The proton phase space hole. The phase space distribution of all proton species at the time . The color scale shows the proton number density . We find a large phase space structure at negative . This structure is not growing further; it has reached its final state.

Image of FIG. 7.
FIG. 7.

(Color online) The electron phase space distribution at the time . The color scale shows the electron number density . We find a strong acceleration of electrons to negative at the leading edge of the proton hole potential.

Image of FIG. 8.
FIG. 8.

(Color online) The final particle energies. (a) Energy distribution of the protons (blue) and the electrons (red) in the jet frame, and (b) protons (blue) and the electrons (red) in the observer frame. All densities are given in the same units. The bin size in (b) is 2000 times larger than in (a). The black line corresponds to a power law with index . It fits the electron distribution in the energy interval limited by two spectral breaks.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Formation of electrostatic structures by wakefield acceleration in ultrarelativistic plasma flows: Electron acceleration to cosmic ray energies