The following results are the outcome of a simulation done with the same setup and diagnostics as in the experiment including the calculated plasma and simulation parameters of sections 6.2 and 6.3. This enables direct comparison to shot 7 carried out during the solenoidal experiment at the Phelix laser system. Before the comparison can be done, the experimental results have to be reprocessed to point out the main features or rather observations. Contrast and brightness changes on the gradation curve are carried out on each layer of the RCF stack shown in figure 5.3 resulting in the modified stack in figure 6.6.
Please note: the modifications are done to make particular features visible and not to distort or adapt the data. The color scale on each layer is different and can not be compared to the other modified films.
Now, observed ring sizes, focus and spot diameters are easier to measure, because of the better contrast.
Furthermore, this illustration clearly shows the analysis problems for radiochromic films with a bad signal-to-noise ratio. Scratches, dust and dirt overvalue the deposited energy in the layer, because it is not possible to remove all noise during the data analysis (more in section 3.3). In additon, the electron signal now emerges especially in layer 3-6. It is in the same horizontal plane as the proton beam but shifted to the right. Due to the symmetry of the experimental setup and the outcoming proton beam, one would expect the same behaviour for the electron beam, but the axis symmetry is broken. Reasons for the aberration could be a slight missalignment of the solenoid, fringe field inhomogeneities, which affect more on the electrons than on the high mass protons, or an unknown external field overlapping the solenoidal fringe field behind the coil exit.
The film stack of the experiment can now be compared to the simulated virtual stack shown in figure 6.7.
In the following, each layer will be analysed separately:
Film #1 — 3.7 MeV: The simulated layer shows the focal, disc and ring structure already observed in the experiment. The focal spot in the center is very intense with the maximum value of the deposited energy of 1.6×107MeV/100×100 µm2. For increasing radius, this peak goes over in a almost flat distribution up to the edge of the disc with a radius of7.4 mm. The radial lineout of layer 1 in figure 6.8 indicates the cut-off of the disc and again the peaked intensity at a radius of14 mm belonging to the observed ring structure. The experimental value of 18.3 mm it is well above this radius, because the ring structure is not so uniform compared to the simulation and hence,
6.5 Comparison of Experiment and Simulation 81
Figure 6.6:Contrast optimized layers of the RCF stack of Phelix shot 7, figure 5.3. The changes on the grada-tion curve result in a clear accentuagrada-tion of the observed proton features. Ring sizes as well as focus and spot diameters are pronounced. The film size is 63.5×63.5 mm2.
the estimated value is an average. Small instabilities in the acceleration mechanism could lead to variations from the symmetric expansion.
Film #2 — 6.6 MeV: At the stack position of 407 mm, the second layer - corresponding to the proton energy of ∼6.6 MeV- is close to the focal plane for these energies. The bulk part of the protons is just before, in or close behind the focus position. The total dimension of the proton spot in this layer is measured to20 mm, which is in good agreement with the simulated value. The virtual detector can measure every single particle regardless of which energy and impact radius. But radiochromic films, as mentioned in section 3.3, have a lower detection threshold. Low energy protons with a large divergence angle will hit the detector in the outer parts and deposit only a tiny fraction of energy. Because the particle density is not very high, the summarized deposited energy is mostly under the detection threshold or so low, that it gets lost during the digitalization process. The observed disc distribution in the simulation with an radius of7.3 mmcould not be observed in the experiment.
Film #3 — 8.7 MeV: The simulation reproduces the ring structure in layer 3 very well. The radius of the ring of10.3 mmis almost the same value calculated for the experiment of11.5 mm. By comparing the images, the hot spot in the center can be confirmed, even if it is not visible in the lineout, because the center of the film was not chosen correctly. The blurring of the proton signal in the area outside the ring differs due to the same effect described above. The density gradient over the ring structure is much lower than in the layers before, but the difference is still observable in the line-out illustration of figure 6.8.
Film #4 - 5 - 6 — 11.7, 14.2, 16.5 MeV: Due to the nature of the proton spectrum, the proton signal in the virtual layer decreases with increasing proton energy, because less particles are available. The total proton spot diameters are similar to the experimental values (50 / 53 / 56 mm), but the still existing intensity enhancement in the center can not be reproduced by the experiment.
82 6 Warp RZ-Simulations of Laser-Accelerated Proton Beams
Figure 6.7:Simulated virtual radiochromic film stack. The given proton energies are exactly the same as for the Phelix shot 7 stack. The simulation data are in very good agreement with the experimental results. Foci, rings and similar proton beam diameters can be observed. The film size is the same as in the experiment 63.5×63.5 mm2 and the logarithmic color scale is in units of deposited energy in MeV per detection area 100×100 µm2.
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Figure 6.8:Radial line-outs for the first three RCF layers of (a) the experiment (figure 6.6) and (b) the siumla-tion with self-fields (figure 6.7). In addisiumla-tion, the simulasiumla-tion results of the run without self-fields is plotted.
6.5 Comparison of Experiment and Simulation 83
Figure 6.8 illustrates the good agreement between experimental and simulated results. However, in some points the simulation without self-fields seems to fit better. More details and explanations about the development of the particular structure in the RCF stack detector are given in the following sections.
Points like particle trajectories, focusing, transport and collimation are discussed when they fit into the context.
After the optical comparison of the observed proton structure in the stack detector, a direct comparison of the deposited energy in each layer is of interest to check the accuracy of the simulation. The films of the experiment given as scanned 16 bit gray-scale images and the simulated virtual layers given in MeV per area on a logarithmic scale are two different descriptions, which can not be absolutely compared.
Therefore, the digitized radiochromic films are converted to the energy deposition description by the help of a proton calibration of the films (see section 3.3). Figure 6.9 shows the comparison of the absolute deposited energy in each layer of the real ( ) and virtual ( ) stack. Using an exponential distributed proton source, one would exactly expect the slope of the simulated data. Less particles deposit their energy in the deeper layers. The simulated deposition can be perfectly repesented by following best-fit curve:
Edep(E) =Edep,0·exp − r E
kBT
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(6.29) with Edep,0 = 4.21×1012 MeV and kBT = 172 keV. For the first three layer, where more energy is deposited, the data sets fit each other very well. For the last three layers, as already pointed out above, the scratches, dust and dirt overvalue the deposited energy. Assuming the undisturbed data would behave like the simulation data, the best-fit curve resulting from the first three points yields to Edep,0 = 4.08×1012 MeV andkBT=162 keV. Within the bounds of the accuracy of the experiment, the absolute values for the energy deposition conform very well to the simulation.
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Figure 6.9:Comparison of the absolute deposited energy in each layer of the real ( ) and virtual ( ) stack.
The plotted factors are the ratios between the simulation and the experiment data. In addition, a simulation without self-fields is plotted in to see the effect of the space charge.
The comparison of the simulation data with the experimental results is far from a detailed explanation of the physical effects responsible for the obtained results. Therefore, the interation of the solenoidal field with charged particles is discussed in the next section. The behaviour of the protons and the electrons is necessary background knowledge before convergence studies are carried out.
84 6 Warp RZ-Simulations of Laser-Accelerated Proton Beams