Peer-Review Publications

2017

D. Seipt, T. Heinzl, M. Marklund, and S. S. Bulanov
Depletion of Intense Fields
Phys. Rev. Lett., 118 :154803 (April 2017)
Abstract:
The interaction of charged particles and photons with intense electromagnetic fields gives rise to multiphoton Compton and Breit-Wheeler processes. These are usually described in the framework of the external field approximation, where the electromagnetic field is assumed to have infinite energy. However, the multiphoton nature of these processes implies the absorption of a significant number of photons, which scales as the external field amplitude cubed. As a result, the interaction of a highly charged electron bunch with an intense laser pulse can lead to significant depletion of the laser pulse energy, thus rendering the external field approximation invalid. We provide relevant estimates for this depletion and find it to become important in the interaction between fields of amplitude a0∼103 and electron bunches with charges of the order of 10 nC.
F. Karbstein
Heisenberg-Euler effective action in slowly varying electric field inhomogeneities of Lorentzian shape
Phys. Rev. D, 95 :076015 (April 2017)
Abstract:
We use a locally constant field approximation (LCFA) to study the one-loop Heisenberg-Euler effective action in a particular class of slowly varying inhomogeneous electric fields of Lorentzian shape with 0≤d<4 inhomogeneous directions. We show that, for these fields, the LCFA of the Heisenberg-Euler effective action can be represented in terms of a single parameter integral, with the constant field effective Lagrangian with rescaled argument as integration kernel. The imaginary part of the Heisenberg-Euler effective action contains information about the instability of the quantum vacuum towards the formation of a state with real electrons and positrons. Here, in particular, we focus on the dependence of the instantaneous vacuum decay rate on the dimension d of the field inhomogeneity. Specifically, for weak fields, we find an overall parametric suppression of the effect with (E0/Ecr)^(d/2), where E0 is the peak field strength of the inhomogeneity and Ecr the critical electric field strength.
V. A. Schanz, F. Wagner, M. Roth, and V. Bagnoud
Noise reduction in third order cross-correlation by angle optimization of the interacting beams
Opt. Express, 25 :9252 (April 2017)
Abstract:
We report on a novel technique to reduce the noise level in scanning third order cross-correlation. Large angles between the interacting beams combined with adapted crystal parameters lead to a significant decrease of noise photon generation while maintaining efficient generation of the third order signal. An enhanced scanning cross-correlator was developed based on the new technique proposed. In tests at the PHELIX laser facility this novel correlator performed within a dynamic range of 12.5 orders of magnitude.
H. Gies, and F. Karbstein
An addendum to the Heisenberg-Euler effective action beyond one loop
J. High Energ. Phys., 03 :108 (March 2017)
Abstract:
We study the effective interactions of external electromagnetic fields induced by fluctuations of virtual particles in the vacuum of quantum electrodynamics. Our main focus is on these interactions at two-loop order. We discuss in detail the emergence of the renowned Heisenberg-Euler effective action from the underlying microscopic theory of quantum electrodynamics, emphasizing its distinction from a standard one-particle irreducible effective action. In our explicit calculations we limit ourselves to constant and slowly varying external fields, allowing us to adopt a locally constant field approximation. One of our main findings is that at two-loop order there is a finite one-particle reducible contribution to the Heisenberg-Euler effective action in constant fields, which was previously assumed to vanish. In addition to their conceptual significance, our results are relevant for high-precision probes of quantum vacuum nonlinearity in strong electromagnetic fields.
H. X. Chang, B. Qiao, T. W. Huang, Z. Xu, C. T. Zhou, Y. Q. Gu, X. Q. Yan, M. Zepf, and X. T. He
Brilliant petawatt gamma-ray pulse generation in quantum electrodynamic laser-plasma interaction
Sci. Rep., 7 :45031 (March 2017)
Abstract:
We show a new resonance acceleration scheme for generating ultradense relativistic electron bunches in helical motions and hence emitting brilliant vortical γ-ray pulses in the quantum electrodynamic (QED) regime of circularly-polarized (CP) laser-plasma interactions. Here the combined effects of the radiation reaction recoil force and the self-generated magnetic fields result in not only trapping of a great amount of electrons in laser-produced plasma channel, but also significant broadening of the resonance bandwidth between laser frequency and that of electron betatron oscillation in the channel, which eventually leads to formation of the ultradense electron bunch under resonant helical motion in CP laser fields. Three-dimensional PIC simulations show that a brilliant γ-ray pulse with unprecedented power of 6.7 PW and peak brightness of 10²⁵ photons/s/mm²/mrad²/0.1% BW (at 15 MeV) is emitted at laser intensity of 1.9 × 10²³ W/cm².
L. Senje, M. Coughlan, D. Jung, M. Taylor, G. Nersisyan, D. Riley, C. L. S. Lewis, O. Lundh, C.-G. Wahlström, M. Zepf, and B. Dromey
Experimental investigation of picosecond dynamics following interactions between laser accelerated protons and water
Appl. Phys. Lett., 110 :104102 (March 2017)
Abstract:
We report direct experimental measurements with picosecond time resolution of how high energy protons interact with water at extreme dose levels (kGy), delivered in a single pulse with the duration of less than 80 ps. The unique synchronisation possibilities of laser accelerated protons with an optical probe pulse were utilized to investigate the energy deposition of fast protons in water on a time scale down to only a few picoseconds. This was measured using absorbance changes in the water, induced by a population of solvated electrons created in the tracks of the high energy protons. Our results indicate that for sufficiently high doses delivered in short pulses, intertrack effects will affect the yield of solvated electrons. The experimental scheme allows for investigation of the ultrafast mechanisms occurring in proton water radiolysis, an area of physics especially important due to its relevance in biology and for proton therapy.
R. Sanchez, M. Lochmann, R. Jöhren, Z. Andelkovic, D. Anielski, B. Botermann, M. Bussmann, A. Dax, N. Frömmgen, C. Geppert, M. Hammen, V. Hannen, T. Kühl, Y. A. Litvinov, R. Lopez-Coto, T. Stöhlker, R. C. Thompson, J. Vollbrecht, W. Wen, C. Weinheimer, E. Will, D. Winters, and W. Nörtershäuser
Laser spectroscopy measurement of the 2s-hyperfine splitting in lithium-like bismuth
J. Phys. B, 50 :085004 (March 2017)
Abstract:
We have recently reported on the first direct measurement of the 2s hyperfine transition in lithium-like bismuth (209Bi^80+) at the GSI Helmholtz Centre for Heavy Ion Research in Darmstadt, Germany. Combined with a new measurement of the 1s hyperfine splitting (HFS) in hydrogen-like (209Bi^82+) the so-called specific difference Δ'E=-61.37(36) meV could be determined and was found to be in good agreement with its prediction from strong-field bound-state quantum electrodynamics. Here we report on additional investigations performed to estimate systematic uncertainties of these results and on details of the experimental setup. We show that the dominating uncertainty arises from insufficient knowledge of the ion beam velocity which is determined by the electron-cooler voltage. Two routes to obtain a cooler-voltage calibration are discussed and it is shown that agreement can be reached either between the experimental Δ'E and the theoretical result, or between the two measurements of the HFS in hydrogen-like bismuth, but not both at the same time.
F. Karbstein
Photon Propagation in Slowly Varying Electromagnetic Fields
Russ. Phys. J., 59 :1 (March 2017)
Abstract:
Effective theory of soft photons in slowly varying electromagnetic background fields is studied at one-loop order in QED. This is of relevance for the study of all-optical signatures of quantum vacuum nonlinearity in realistic electromagnetic background fields as provided by high-intensity lasers. The central result derived in this article is a new analytical expression for the photon polarization tensor in two linearly polarized counterpropagating pulsed Gaussian laser beams. Treating the peak field strengths of both laser beams as free parameters, this field configuration can be considered as interpolating between the limiting cases of a purely right- or left-moving laser beam (if one of the peak field strengths is set equal to zero) and the standing-wave type scenario with two counter-propagating beams of equal strength.
J. Deprince, S. Fritzsche, T. Kallman, P. Palmeri, and P. Quinet
Plasma effects on atomic data for the K-vacancy states of highly charged iron ions
AIP Conf. Proc., 1811 :040002 (March 2017)
Abstract:
The main goal of the present work is to estimate the effects of plasma environment on the atomic parameters associated with the K-vacancy states in highly charged iron ions within the astrophysical context of accretion disks around black holes. In order to do this, multiconfiguration Dirac-Fock computations have been carried out by considering a time averaged Debye-Hückel potential for both the electron-nucleus and electron-electron interactions. In the present paper, a first sample of results related to the ionization potentials, the K-thresholds, the transition energies and the radiative emission rates is reported for the ions Fe23+ and Fe24+.
M. Wünsche, S. Fuchs, S. Aull, J. Nathanael, M. Möller, C. Rödel, and G.G. Paulus
Quasi-supercontinuum source in the extreme ultraviolet using multiple frequency combs from high-harmonic generation
Opt. Express, 25 :6936 (March 2017)
Abstract:
A quasi-supercontinuum source in the extreme ultraviolet (XUV) is demonstrated using a table-top femtosecond laser and a tunable optical parametric amplifier (OPA) as a driver for high-harmonic generation (HHG). The harmonic radiation, which is usually a comb of odd multiples of the fundamental frequency, is generated by near-infrared (NIR) laser pulses from the OPA. A quasi-continuous XUV spectrum in the range of 30 to 100 eV is realized by averaging over multiple harmonic comb spectra with slightly different fundamental frequencies and thus different spectral spacing between the individual harmonics. The driving laser wavelength is swept automatically during an averaging time period. With a total photon flux of 4×10^9 photons/s in the range of 30 eV to 100 eV and 1×10^7photons/s in the range of 100 eV to 200 eV, the resulting quasi-supercontinuum XUV source is suited for applications such as XUV coherence tomography (XCT) or near-edge absorption fine structure spectroscopy (NEXAFS).
S. Galyamin, A. Tyukhtin, and A. Peshkov
Transition radiation at the boundary of a chiral isotropic medium
Phys. Rev. E, 95 :032142 (March 2017)
Abstract:
This study analyzes the radiation produced by a point charge intersecting the interface between a vacuum and a chiral isotropic medium. We deduce analytical expressions for the Fourier components of an electromagnetic field in both vacuum and medium for arbitrary charge velocity. The main focus is on investigating the far field in a vacuum. The distinguishing feature of the interface with a chiral isotropic medium is that the field in the vacuum area contains both copolarization (coinciding with the polarization of the self-field of a charge) and cross-polarization (orthogonal to the polarization of the self-field). Using a saddle-point approach, we obtain asymptotic representations for the field components in the far-field zone for typical frequency ranges of the Condon model of the chiral medium. We note that a so-called lateral wave is generated in a vacuum for certain parameters. The main contribution to the radiation at large distances is presented by two (co- and cross-) spherical waves of transition radiation. These waves are coherent and result in a total spherical wave with elliptical polarization, with the polarization coefficient being determined by the chirality of the medium. We present typical radiation patterns and ellipses of polarization.
Z. Samsonova, S. Höfer, A. Hoffmann, B. Landgraf, M. Zürch, I. Uschmann, D. Khaghani, O. Rosmej, P. Neumayer, R. Röder, L. Trefflich, C. Ronning, E. Förster, C. Spielmann, and D. Kartashov
X-ray emission generated by laser-produced plasmas from dielectric nanostructured targets
AIP Conf. Proc., 1811 :180001 (March 2017)
Abstract:
We present an experimental study of X-ray generation from nanostructured ZnO targets. Samples of different morphology ranging from nanowires to polished surfaces are irradiated by relativistically intense femtosecond laser pulses. X-ray emission of plasma is generated by 45 fs 130 mJ laser pulses at 400 nm with picosecond temporal contrast better than 1E−9 interacting with an array of ZnO nanowires. The measured spectra indicate the existence of highly ionized states of Zn (up to He-like Zn). The obtained flux of ∼1E10 photons per laser shot at the neutral Zn Kα energies around 8.65 keV and at the Zn Heα energies around 9 keV is almost 3 times higher for nanostructured targets compared to the reference polished sample and implies 1E−4 conversion efficiency from the laser energy to the total energy of the emitted X-ray photons.
F. Wagner, J. Hornung, C. Schmidt, M. Eckhardt, M. Roth, T. Stöhlker, and V. Bagnoud
Backreflection diagnostics for ultra-intense laser plasma experiments based on frequency resolved optical gating
Rev. Sci. Instrum., 88 :023503 (February 2017)
Abstract:
We report on the development and implementation of a time resolved backscatter diagnostics for high power laser plasma experiments at the petawatt-class laser facility PHELIX. Pulses that are backscattered or reflected from overcritical plasmas are characterized spectrally and temporally resolved using a specially designed second harmonic generation frequency resolved optical gating system. The diagnostics meets the requirements made by typical experiments, i.e., a spectral bandwidth of more than 30nm with sub-nanometer resolution and a temporal window of 10ps with 50fs temporal resolution. The diagnostics is permanently installed at the PHELIX target area and can be used to study effects such as laser-hole boring or relativistic self-phase-modulation which are important features of laser-driven particle acceleration experiments.
N. Winckler, A. Rybalchenko, V. Shevelko, M. Al-Turany, T. Kollegger, and T. Stöhlker
BREIT code: Analytical solution of the balance rate equations for charge-state evolutions of heavy-ion beams in matter
Nucl. Instr. Meth. Phys. Res. B, 392 :67 (February 2017)
Abstract:
A detailed description of a recently developed BREIT computer code (Balance Rate Equations of Ion Transportation) for calculating charge-state fractions of ion beams passing through matter is presented. The code is based on the analytical solutions of the differential balance equations for the charge-state fractions as a function of the target thickness and can be used for calculating the ion evolutions in gaseous, solid and plasma targets. The BREIT code is available on-line and requires the charge-changing cross sections and initial conditions in the input file. The eigenvalue decomposition method, applied to obtain the analytical solutions of the rate equations, is described in the paper. Calculations of non-equilibrium and equilibrium charge-state fractions, performed by the BREIT code, are compared with experimental data and results of other codes for ion beams in gaseous and solid targets. Ability and limitations of the BREIT code are discussed in detail.
M. Gebhardt, C. Gaida, F. Stutzki, S. Hädrich, C. Jauregui, J. Limpert, and A. Tünnermann
High average power nonlinear compression to 4 GW, sub-50  fs pulses at 2 μm wavelength
Opt. Lett., 42 :747 (February 2017)
Abstract:
The combination of high-repetition-rate ultrafast thulium-doped fiber laser systems and gas-based nonlinear pulse compression in waveguides offers promising opportunities for the development of high-performance few-cycle laser sources at 2 μm wavelength. In this Letter, we report on a nonlinear pulse compression stage delivering 252 μJ, sub-50 fs-pulses at 15.4 W of average power. This performance level was enabled by actively mitigating ultrashort pulse propagation effects induced by the presence of water vapor absorptions.
D. Wu, X. T. He, W. Yu, and S. Fritzsche
Monte Carlo approach to calculate ionization dynamics of hot solid-density plasmas within particle-in-cell simulations
Phys. Rev. E, 95 :023208 (February 2017)
Abstract:
A physical model based on a Monte Carlo approach is proposed to calculate the ionization dynamics of hot-solid-density plasmas within particle-in-cell (PIC) simulations, and where the impact (collision) ionization (CI), electron-ion recombination (RE), and ionization potential depression (IPD) by surrounding plasmas are taken into consideration self-consistently. When compared with other models, which are applied in the literature for plasmas near thermal equilibrium, the temporal relaxation of ionization dynamics can also be simulated by the proposed model. Besides, this model is general and can be applied for both single elements and alloys with quite different compositions. The proposed model is implemented into a PIC code, with (final) ionization equilibriums sustained by competitions between CI and its inverse process (i.e., RE). Comparisons between the full model and model without IPD or RE are performed. Our results indicate that for bulk aluminium at temperature of 1 to 1000 eV, (i) the averaged ionization degree increases by including IPD; while (ii) the averaged ionization degree is significantly over estimated when the RE is neglected. A direct comparison from the PIC code is made with the existing models for the dependence of averaged ionization degree on thermal equilibrium temperatures and shows good agreements with that generated from Saha-Boltzmann model and/or FLYCHK code.
D. Wu, X. T. He, W. Yu, and S. Fritzsche
Monte Carlo approach to calculate proton stopping in warm dense matter within particle-in-cell simulations
Phys. Rev. E, 95 :023207 (February 2017)
Abstract:
A Monte Carlo approach to proton stopping in warm dense matter is implemented into an existing particle-in-cell code. This approach is based on multiple electron-electron, electron-ion, and ion-ion binary collision and accounts for both the free and the bound electrons in the plasmas. This approach enables one to calculate the stopping of particles in a more natural manner than existing theoretical treatment. In the low-temperature limit, when “all” electrons are bound to the nucleus, the stopping power coincides with the predictions from the Bethe-Bloch formula and is consistent with the data from the National Institute of Standard and Technology database. At higher temperatures, some of the bound electrons are ionized, and this increases the stopping power in the plasmas, as demonstrated by A. B. Zylstra et al. [Phys. Rev. Lett. 114, 215002 (2015)]. At even higher temperatures, the degree of ionization reaches a maximum and thus decreases the stopping power due to the suppression of collision frequency between projected proton beam and hot plasmas in the target.
P. Wustelt, M. Möller, M. Schöffler, X. Xie, V. Hanus, A. Sayler, A. Baltuska, G. Paulus, and M. Kitzler
Numerical investigation of the sequential-double-ionization dynamics of helium in different few-cycle-laser-field shapes
Phys. Rev. A, 95 :023411 (February 2017)
Abstract:
We investigate sequential double ionization of helium by intense near-circularly polarized few-cycle laser pulses using a semiclassical ionization model with two independent electrons. Simulated He^2+ ion momentum distributions are compared to those obtained in recent benchmark experiments. We study the influence of a number of pulse parameters such as peak intensity, carrier-envelope phase, pulse duration, and second- and third-order spectral phase on the shape of the ion momentum distributions. Good agreement is found in the main features of these distributions and of their dependence on the laser pulse duration, peak intensity, and carrier-envelope phase. Furthermore, we find that for explaining certain fine-scale features observed in the experiments, it becomes important to consider subtle timing variations in the two-electron emissions introduced by small values of chirp. This result highlights the possibility of measuring and controlling multielectron dynamics on the attosecond time scale by fine tuning the field evolution of intense close-to-single-cycle laser pulses.
M. Kasim, L. Ceurvorst, N. Ratan, J. Sadler, N. Chen, A. Sävert, R. Trines, R. Bingham, P. Burrows, M. Kaluza, and P. Norreys
Quantitative shadowgraphy and proton radiography for large intensity modulations
Phys. Rev. E, 95 :023306 (February 2017)
Abstract:
Shadowgraphy is a technique widely used to diagnose objects or systems in various fields in physics and engineering. In shadowgraphy, an optical beam is deflected by the object and then the intensity modulation is captured on a screen placed some distance away. However, retrieving quantitative information from the shadowgrams themselves is a challenging task because of the nonlinear nature of the process. Here, we present a method to retrieve quantitative information from shadowgrams, based on computational geometry. This process can also be applied to proton radiography for electric and magnetic field diagnosis in high-energy-density plasmas and has been benchmarked using a toroidal magnetic field as the object, among others. It is shown that the method can accurately retrieve quantitative parameters with error bars less than 10%, even when caustics are present. The method is also shown to be robust enough to process real experimental results with simple pre- and postprocessing techniques. This adds a powerful tool for research in various fields in engineering and physics for both techniques.
D. Adolph, M. Möller, J. Bierbach, M. Schwab, A. Sävert, M. Yeung, A. M. Sayler, M. Zepf, M.C. Kaluza, and G.G. Paulus
Real-time, single-shot, carrier-envelope-phase measurement of a multi-terawatt laser
Appl. Phys. Lett., 110 :081105 (February 2017)
Abstract:
We present the single-shot carrier-envelope phase (CEP) determination of a 1 Hz, multi-terawatt (TW) laser system with a setup based on spectral broadening in a hollow-core fiber and a stereographic measurement of the energy-dependent above-threshold ionization plateau. The latter is extremely sensitive to variations in CEP. As compared to the f-2f interferometers, this technique reduces the uncertainties due to the shot-to-shot intensity fluctuations, which are prevalent in the TW laser systems. The experimental results pave the way towards the investigation and control over CEP-sensitive processes at ultra-high intensities.
L. Deák, L. Bottyán, T. Fülöp, D. G. Merkel, D. L. Nagy, S. Sajti, K. S. Schulze, H. Spiering, I. Uschmann, and H.-C. Wille
Realizing total reciprocity violation in the phase for photon scattering
Sci. Rep., 7 :43114 (February 2017)
Abstract:
Reciprocity is when wave or quantum scattering satisfies a symmetry property, connecting a scattering process with the reversed one. While reciprocity involves the interchange of source and detector, it is fundamentally different from rotational invariance, and is a generalization of time reversal invariance, occurring in absorptive media as well. Due to its presence at diverse areas of physics, it admits a wide variety of applications. For polarization dependent scatterings, reciprocity is often violated, but violation in the phase of the scattering amplitude is much harder to experimentally observe than violation in magnitude. Enabled by the advantageous properties of nuclear resonance scattering of synchrotron radiation, we have measured maximal, i.e., 180-degree, reciprocity violation in the phase. For accessing phase information, we introduced a new version of stroboscopic detection. The scattering setting was devised based on a generalized reciprocity theorem that opens the way to construct new types of reciprocity related devices.
P. Hansinger, P. Töpfer, N. Dimitrov, D. Adolph, D. Hoff, T. Rathje, A. M. Sayler, A. Dreischuh, and G.G. Paulus
Refractive index dispersion measurement using carrier-envelope phasemeters
New J. Phys., 19 :023040 (February 2017)
Abstract:
We introduce a novel method for direct and accurate measurement of refractive index dispersion based on carrier-envelope phase detection of few-cycle laser pulses, exploiting the difference between phase and group velocity in a dispersive medium. In a layout similar to an interferometer, two carrier-envelope phasemeters are capable of measuring the dispersion of a transparent or reflective sample, where one phasemeter serves as the reference and the other records the influence of the sample. Here we report on proof-of-principle measurements that already reach relative uncertainties of a few 10^−4 . Further development is expected to allow for unprecedented precision.
D. Zille, D. Seipt, M. Möller, S. Fritzsche, S. Gräfe, C. Müller, and G.G. Paulus
Spin-dependent rescattering in strong-field ionization of helium
J. Phys. B, 50 :065001 (February 2017)
Abstract:
We investigate the influence of singlet and triplet spin states on rescattered photoelectrons in strong-field ionization of excited helium. Choosing either a symmetric or antisymmetric spatial wave function as the initial state results in different scattering cross sections for the 1s2s¹S and ³S states. These cross sections are used in the semi-classical model of strong-field ionization. Our investigations show that the photoelectron momentum distributions of rescattered electrons exhibit a significant dependence on the relative spin state of the projectile and the bound electron which should be observable in experiments. The proposed experimental approach can be understood as a testbed for probing the spin dynamics of electrons during strong-field ionization and the presented results as a baseline for their identification.
R. Ferrer, A. Barzakh, B. Bastin, R. Beerwerth, M. Block, P. Creemers, H. Grawe, R. Groote, P. Delahaye, X. Fléchard, S. Franchoo, S. Fritzsche, L. P. Gaffney, L. Ghys, W. Gins, C. Granados, R. Heinke, L. Hijazi, M. Huyse, T. Kron, Y. Kudryavtsev, M. Laatiaoui, N. Lecesne, M. Loiselet, F. Lutton, I. D. Moore, Y. Martínez, E. Mogilevskiy, P. Naubereit, J. Piot, S. Raeder, S. Rothe, H. Savajols, S. Sels, V. Sonnenschein, J.-C. Thomas, E. Traykov, C. Beveren, P. Bergh, P. Duppen, K. Wendt, and A. Zadvornaya
Towards high-resolution laser ionization spectroscopy of the heaviest elements in supersonic gas jet expansion
Nat. Commun., 8 :14520 (February 2017)
Abstract:
Resonant laser ionization and spectroscopy are widely used techniques at radioactive ion beam facilities to produce pure beams of exotic nuclei and measure the shape, size, spin and electromagnetic multipole moments of these nuclei. However, in such measurements it is difficult to combine a high efficiency with a high spectral resolution. Here we demonstrate the on-line application of atomic laser ionization spectroscopy in a supersonic gas jet, a technique suited for high-precision studies of the ground- and isomeric-state properties of nuclei located at the extremes of stability. The technique is characterized in a measurement on actinium isotopes around the N=126 neutron shell closure. A significant improvement in the spectral resolution by more than one order of magnitude is achieved in these experiments without loss in efficiency.
J. Thomas, M. M. Günther, and A. Pukhov
Beam load structures in a basic relativistic interaction model
Phys. Plasmas, 24 :013101 (January 2017)
Abstract:
Some recent experiments have shown that the beam load in bubble and blow-out experiments is located in a volume as small as a few μm^3. Now, we show what kinds of inner structures are possible in such a high dense electron ensemble. Our analysis starts from a first principles model for relativistically corrected mutual electron interaction in a phenomenological bubble model. Discussing 2D and 3D beam load configurations, we show that, depending on the bunch emittance, the beam load might be in a highly ordered and dense configuration, a less ordered but still dense state, or a configuration where each electron performs an individual random motion.