Plots of target electron density lineouts along the laser axis and the fitted power law functions (see Table I) used to describe the density profile in OSIRIS. (a) Small density scalelength and (b) large density scalelength.
Rear surface temperatures as a function of target thickness for the three experimental density scalelengths: (a) HISAC pyrometry and (b) K α spectroscopy. Actual data points are shown with hollow symbols, while the errors bars depict the standard deviation from the mean (shown by solid symbols). (c) Comparison of mean pyrometry data from this experiment against previously published experimental results. Note all data on plot (c) are normalized to laser energy on target.
Emission spot size HWHM as a function of target thickness: (a) 2D Cu k α imager and (b) HISAC thermal emission. The HWHM of both emission regions is reduced with increasing density scalelength, the reduction in the thermal dataset is greater.
Integrated emission as a function of target thickness and density scalelength: (a) spatial integral of HISAC thermal signal showing no clear trends as a function of density scalelength and (b) spectrally integrated spectrometer signal, showing the small density scalelength signal is largest. Note to aid comparison, all data have been normalized to a shot energy of 50 J.
Spatially integrated emission of the diagnostics most sensitive to the higher energy electrons as a function of target thickness and density scalelength: (a) spatially integrated OTR and (b) Cu K α imager background.
Channelling by, and subsequent refraction of the laser beam in the large density scalelength underdense plasma as it approaches the 45° p-polarised 40nc target (top right). The effective target thickness (t) is depicted. Only part of the simulation box is shown.
Phase space plots showing the momentum components parallel (p1), and transverse (p2), with respect to the laser injection axis at time —the pulse is at 0.5nc , just 4 μm from nc : (a) small density scalelength and (b) large density scalelength.
PIC modelling results: (a) The electron number distribution function integrated from the earlier time to the time shown, e.g., the data denoted time is the fast electron number distribution function injected by the laser between 1370 and 2050. At early times, the large density scalelength accelerates considerably more electrons to a given energy. Over the whole simulation, the short density scalelength interaction accelerates a higher number of electrons to the lowest energies. (b) Integrals of the electron energy distribution function from the previous time to the time shown. Here the trends are similar to those in (a).
(a)–(d) PIC modelling results showing the angular distribution of the electron energy integrated from the earlier time to the time shown, e.g., the data denoted time is the fast electron energy angular distribution function injected by the laser between 1370 and 1632. 0° is the laser axis, the target plane is shown. At early times, (a) the laser is too low for the electrons to be accelerated forwards by the push. Later (b)–(c) when the laser is more intense and still propagating in the sub-solid density plasma, there is a significant amount of energy peaked either side of the laser axis. This is the “collimated” fast electron pre-beam component; it is considerably enhanced with the large density scalelength. The electron energy distribution created at late time (d) is near isotropic, and this is in part due to the refraction of the laser in the underdense plasma, which causes the laser to change direction, accelerating electrons in many directions.
The effect of density scalelength on the fast electron pre-beam: (a) the fast electron current in the pre-beam () normalised to the total absorbed current () over the whole small density scalelength run. The current in the large density scalelength case is higher during the pre-beam stage, while during the main-beam (laser-solid interaction) the small density scalelength current is highest, generating the largest total current. The current was found to be basically identical to the electron number. (b) The mean electron kinetic energy in the pre-beam, and that in the outer cone of the forward hemisphere (). The large density scalelength pre-beam is significantly hotter than that of the small density scalelength pre-beam. The interaction of the laser pulse with the plasma near the target front surface causes the rise in kinetic energy to stagnate then fall. The mean energies of the forward going electrons not in the pre-beam are also shown. They are similar for both density scalelengths and of lower energy than those in the pre-beam—the fast electron mean energy has angular dependance. The peak in the laser intensity occurs at . (c) The energy in the pre-beam normalized to the total absorbed fast electron energy over the whole run. Until the very end of the run there is more energy in the large density scalelength case (the pre-beam is enhanced). For both density scalelengths, the total energy absorbed into the forward hemisphere of fast electrons was identical.
All plots shown at the end of the pre-beam, due to symmetry only half of each image is shown. Top row: target electron temperature, bottom row: magnetic field. Left column: large density scalelength, right column: small density scalelength. (a) The large density scalelength fast electron pre-beam heats the target at a depth of 20 μm by ∼8 eV—considerably less than that observed experimentally (note the initial target temperature was set to 50 eV). (b) shows the small density scalelength fast electron pre-beam heats the target at a depth of 20 μm by ∼5 eV. (c) The magnetic field generated by the large density scalelength pre-beam is significantly larger than that in (d).
(Top row) target temperatures, (bottom row) magnetic field, all images 400 fs after the arrival of the fast electron main-beam: (left) no pre-beam, (middle) small density scalelength pre-beam, (right) large density scalelength pre-beam. The large density scalelength enhances the magnetic fields and consequently the target temperatures ((f) and (c), respectively), in qualitative agreement with the experimental results.
The shot parameters for the three experimental density scalelengths and the functions fitted to the front surface density profiles. The functions fit the front surface density profiles along the propagation axis of the laser (45° off target normal), x (in μm) is zero at the initial target front surface and decreases along the (outward) target normal axis. The functions were bounded at the target solid surface, switching to the target solid density.
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