Various elliptic orbits of the form intersecting , and , and .
The longitudinal momentum of an electron in the boosted frame as a function of position in the bubble in the laboratory frame, according to Eq. (20) for .
Graph showing the variation of transverse momentum with transverse position in the bubble, for . The solid line shows the solution of Eq. (37) and the dashed line is the expanded solution, Eq. (38).
Geometry of trajectory in laboratory frame of electron performing a circular arc trajectory with arbitrary radius , but which intercepts the points , and , and .
(a) Graph of the on-axis spectral intensity, calculated from (i) the synchrotronlike spectrum given by Eq. (56), and (ii) Eq. (58) for a synchrotron spectrum emission by an electron with varying energy. (iii) shows a synchrotronlike spectrum with the same peak energy and amplitude as (ii), which a critical frequency and an amplitude of 0.69 of (i). (b) shows the spectra calculated using the code RADAMPELTRAC (Ref. 26) from (i) 17.3 (i.e., ) oscillations of an electron with Lorentz factor and transverse momentum in a radial electric field and (ii) an electron accelerating in a bubble to maximum transverse oscillations and energy of , . is the frequency of the drive laser (not included in the numerical modeling).
The scaling of the critical energy of photons emitted in the plasma bubbletron as a function of the electron number density and the laser driver field strength parameter .
The scaling of the spectral brightness of photons emitted by the plasma bubbletron as a function of the electron number density and the laser driver field strength parameter .
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