Peer-Review Publications


P. Zhang, S. S. Bulanov, D. Seipt, A. V. Arefiev, and A. G. R. Thomas
Relativistic plasma physics in supercritical fields
Phys. Plasmas, 27 :050601 (May 2020)
Since the invention of chirped pulse amplification, which was recognized by a Nobel prize in physics in 2018, there has been a continuing increase in available laser intensity. Combined with advances in our understanding of the kinetics of relativistic plasma, studies of laser-plasma interactions are entering a new regime where the physics of relativistic plasmas is strongly affected by strong-field quantum electrodynamics (QED) processes, including hard photon emission and electron-positron (e^+-e^−) pair production. This coupling of quantum emission processes and relativistic collective particle dynamics can result in dramatically new plasma physics phenomena, such as the generation of dense e^+-e^− pair plasma from near vacuum, complete laser energy absorption by QED processes or the stopping of an ultrarelativistic electron beam, which could penetrate a cm of lead, by a hair's breadth of laser light. In addition to being of fundamental interest, it is crucial to study this new regime to understand the next generation of ultra-high intensity laser-matter experiments and their resulting applications, such as high energy ion, electron, positron, and photon sources for fundamental physics studies, medical radiotherapy, and next generation radiography for homeland security and industry.
D. Wu, W. Yu, Z. Sheng, S. Fritzsche, and X. He
Uniform warm dense matter formed by direct laser heating in the presence of external magnetic fields
Phys. Rev. E, 101 :051202 (May 2020)
With the recent realization of kilotesla quasistatic magnetic fields, the interaction of a laser with magnetized solids enters an unexplored new regime. In particular, a circularly polarized (CP) laser pulse may propagate in a highly magnetized plasma of any high density without encountering cutoff reflection in the whistler mode. With this, we propose a scheme for producing uniform warm dense matter (WDM) by direct laser heating with a CP laser irradiating onto the target along the magnetic field. It is shown by particle-in-cell simulations, which include advanced ionization dynamics and collision dynamics, moderately intense right-hand CP laser light at 1015W/cm2 can propagate in solid aluminum and heat it efficiently to the 100 eV level within picoseconds. By using two laser pulses irradiating from two sides of a thin solid target, uniform heating to WDM can be achieved. This provides a controllable way to create WDM at different temperatures.
A. Mayer, J. Fellinger, W. Grosinger, G. Winkler, L. Perner, C. Heyl, I. Hartl, and O. Heckl
Versatile Figure-9 Design: How to Access Low-Noise Regimes in an All-PM Yb:Fiber Laser
Conference Proceedings - Lasers and Electro-Optics Society Annual Meeting-LEOS (May 2020)
V. Hilbert, M. Tschernajew, R. Klas, J. Limpert, and J. Rothhardt
A compact, turnkey, narrow-bandwidth, tunable, and high-photon-flux extreme ultraviolet source
AIP Adv., 10 :045227 (April 2020)
We report on a compact high-photon-flux extreme ultraviolet (XUV) source based on high harmonic generation. A high XUV-photon flux (>10¹³ photons/s) is achieved at 21.8 eV and 26.6 eV. The narrow spectral bandwidth (ΔE/E < 10⁻³) of the generated harmonics is in the range of state-of-the-art synchrotron beamlines and enables high resolution spectroscopy experiments. The robust design based on a fiber– laser system enables turnkey-controlled and even remotely controlled operation outside specialized laser laboratories, which opens the way for a variety of applications.
E. Appi, C. C. Papadopoulou, J. L. Mapa, N. Wesavkar, C. Jusko, P. Mosel, S. Ališauskas, T. Lang, C. M. Heyl, B. Manschwetus, M. Brachmanski, M. Braune, H. Lindenblatt, F. Trost, S. Meister, P. Schoch, R. Treusch, R. Moshammer, I. Hartl, U. Morgner, and M. Kovacev
A synchronized VUV light source based on high-order harmonic generation at FLASH
Sci. Rep., 10 :6867 (April 2020)
Ultrafast measurements in the extreme ultraviolet (XUV) spectral region targeting femtosecond timescales rely until today on two complementary XUV laser sources: free electron lasers (FELs) and high-harmonic generation (HHG) based sources. The combination of these two source types was until recently not realized. The complementary properties of both sources including broad bandwidth, high pulse energy, narrowband tunability and femtosecond timing, open new opportunities for two-color pump-probe studies. Here we show first results from the commissioning of a high-harmonic beamline that is fully synchronized with the free-electron laser FLASH, installed at beamline FL26 with permanent end-station including a reaction microscope (REMI). An optical parametric amplifier synchronized with the FEL burst mode drives the HHG process. First commissioning tests including electron momentum measurements using REMI, demonstrate long-term stability of the HHG source over more than 14 hours. This realization of the combination of these light sources will open new opportunities for time-resolved studies targeting different science cases including core-level ionization dynamics or the electron dynamics during the transformation of a molecule within a chemical reaction probed on femtosecond timescales in the ultraviolet to soft X-ray spectral region.
B. Baghdasaryan, F. Steinlechner, and S. Fritzsche
Characterization of opening angle correlations of a biphoton state decomposed in Bessel modes
Phys. Rev. A, 101 :043844 (April 2020)
The spontaneous parametric down-conversion of photons has been widely applied for generating entangled photon pairs. We theoretically explore the entangled down-converted state of the photon pair, also known as biphoton state, for both degenerate and nondegenerate photon pairs. In particular, the spatial structure of the biphoton state has been expressed in Bessel modes to better understand the correlation with regard to the opening angle Ï'k of Bessel modes. In fact, the opening angles of the down-converted photon pair are not independent of each other, but rather are correlated. Furthermore, we confirm the experimentally observed conditions concerning the optimization of generating high-degree spatial entanglement by controlling the beam waist of the pump beam. We also introduce a new experimental setup for efficient measurement of the spatial entanglement of the biphoton state using geometrical optics arguments.
K. Schoenberg, V. Bagnoud, A. Blazevic, V. E. Fortov, D. O. Gericke, A. Golubev, D. H. H. Hoffmann, D. Kraus, I. V. Lomonosov, V. Mintsev, S. Neff, P. Neumayer, A. R. Piriz, R. Redmer, O. Rosmej, M. Roth, T. Schenkel, B. Sharkov, N. A. Tahir, D. Varentsov, and Y. Zhao
High-energy-density-science capabilities at the Facility for Antiproton and Ion Research
Phys. Plasmas, 27 :043103 (April 2020)
The Facility for Antiproton and Ion Research (FAIR) will employ the World's highest intensity relativistic beams of heavy nuclei to uniquely create and investigate macroscopic (millimeter-sized) quantities of highly energetic and dense states of matter. Four principal themes of research have been identified: properties of materials driven to extreme conditions of pressure and temperature, shocked matter and material equation of state, basic properties of strongly coupled plasma and warm dense matter, and nuclear photonics with a focus on the excitation of nuclear processes in plasmas, laser-driven particle acceleration, and neutron production. The research program, principally driven by an international collaboration of scientists, called the HED@FAIR collaboration, will evolve over the next decade as the FAIR project completes and experimental capabilities develop. The first programmatic research element, called “FAIR Phase 0, officially began in 2018 to test components, detectors, and experimental techniques. Phase-0 research employs the existing and enhanced infrastructure of the GSI Helmholtzzentrum für Schwerionenforschung (GSI) heavy-ion synchrotron coupled with the PHELIX high-energy, high-intensity laser. The “FAIR Day one” experimental program, presently scheduled to begin in 2025, commences the use of FAIR's heavy-ion synchrotron, coupled to new experimental and diagnostic infrastructure, to realize the envisaged high-energy-density-science research program.
J. Deprince, M. Bautista, S. Fritzsche, J. García, T. Kallman, C. Mendoza, P. Palmeri, and P. Quinet
K-line X-ray fluorescence from highly charged iron ions under dense astrophysical plasma conditions
X-Ray Spec., 49 :29 (April 2020)
In the present work, we report an investigation of plasma environment effects 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. More particularly, the sensitivity of K-line X-ray fluorescence parameters (wavelengths, radiative transition probabilities, and Auger rates) in Fe XVII–Fe XXV ions has been estimated for plasma conditions characterized by an electron temperature ranging from 10⁵ to 10⁷ K and an electron density ranging from 10¹⁸ to 10²² cm⁻³. In order to do this, relativistic multiconfiguration Dirac-Fock atomic structure calculations have been carried out by considering a time averaged Debye-Hückel potential for both the electron–nucleus and electron–electron interactions.
O. Forstner, J. Müller, and K. Stiebing
Opportunities for negative ions studies at the Frankfurt Low-energy Storage Ring (FLSR)
Hyperfine Interact., 241 :53 (April 2020)
The room-temperature electrostatic heavy ion storage ring FLSR was originally designed to study the collision dynamics of atoms and molecules. Recently it has been equipped with a RF plasma ion source combined with a charge exchange cell to be able to perform studies with negative ions in the ring. In preliminary experiments beams of He−, O− and OH− could successfully be stored. The measured lifetime of the metastable He−—ion is in good agreement with previous results, showing that the lifetime measurement in this case is not limited by the storage time due to collisional detachment. In the case of O− and OH− storage times in the order of seconds have been achieved. In a next step laser beams will be introduced in the ring allowing photodetachment studies of vibrationally cold molecules.
S. Kosugi, F. Koike, T. Nagayasu, F. Hosseini, J. Martins, T. Marchenko, O. Travnikova, M. Oura, T. Gejo, J. Harries, J. Bozek, K. Ito, E. Sokell, S. Fritzsche, M. Piancastelli, M. Simon, and Y. Azuma
Strong configuration interaction in the 3p photoelectron spectrum of Kr
Phys. Rev. A, 101 :042505 (April 2020)
We measured the Kr photoelectron spectrum in the region close to the 3p ionization threshold. Our high-resolution measurements allowed a clear observation of spectral structures due to electron correlation effects. Analysis based on relativistic multiconfiguration calculations could explain these observed peaks as due to strong configuration interactions between the 3p-1 state and 3d-2nl states. Calculated and experimental data for peak assignments and intensity distributions are in good agreement. In addition, we measured the anisotropy parameter β, which also agreed well with theory. These findings provide a detailed view of strong configuration interactions between the 3p-1 and 3d-2nl inner-shell hole states.
S. Schippers, T. Buhr, A. Borovik Jr., K. Holste, A. Perry-Sassmannshausen, K. Mertens, S. Reinwardt, M. Martins, S. Klumpp, K. Schubert, S. Bari, R. Beerwerth, S. Fritzsche, S. Ricz, J. Hellhund, and A. Müller
The photon-ion merged-beams experiment PIPE at PETRA III—The first five years
X-Ray Spec., 49 :11 (April 2020)
The Photon-Ion Spectrometer at PETRA III—in short, PIPE—is a permanently installed user facility at the 'Variable Polarization XUV Beamline' P04 of the synchrotron light source PETRA III operated by DESY in Hamburg, Germany. The careful design of the PIPE ion-optics in combination with the record-high photon flux at P04 has lead to a breakthrough in experimental studies of photon interactions with ionized small quantum systems. This short review provides an overview over the published scientific results from photon-ion merged-beams experiments at PIPE that were obtained since the start of P04 operations in 2013. The topics covered comprise photoionization of ions of astrophysical relevance, quantitative studies of multi-electron processes upon inner-shell photoexcitation and photoionization of negative and positive atomic ions, precision spectroscopy of photoionization resonances, photoionization and photofragmentation of molecular ions, and of endohedral fullerene ions.
C. Hahn, E. Menz, P. Pfäfflein, G. Weber, and T. Stöhlker
A scintillator‐based particle detector for CRYRING@ESR
X-Ray Spec., 49 :338 (March 2020)
With the unprecedented range of ion species and energies offered by the newly commissioned CRYRING facility, the availability of single ion detectors is of significant importance as part of standard instrumentation as well as for novel experiments. A detector system was constructed on the basis of the YAP:Ce crystal scintillator, which is at once radiation‐hard, fast, and affordable. Results of a characterization experiment confirmed the feasibility of the setup for incident ion rates on the order of MHz and found a critical fluence of some 10¹³ cm⁻² upon which the crystal is rendered locally blind to further ion irradiation. The device was first used in CRYRING commissioning runs in August and November 2018. Future efforts will complete the integration of the detector into the GSI control and data acquisition system MBS.
D. Würzler, S. Skruszewicz, A. M. Sayler, D. Zille, M. Möller, P. Wustelt, Y. Zhang, J. Tiggesbäumker, and G.G. Paulus
Accurate retrieval of ionization times by means of the phase-of-the-phase spectroscopy, and its limits
Phys. Rev. A, 101 :033416 (March 2020)
By applying recently introduced, phase-of-the-phase spectroscopy [S. Skruszewicz et al., Phys. Rev. Lett. 115, 043001 (2015)], we analyze the phase-dependent photoelectron signal from Xe ionized in intense, parallel, two-color (1800 nm and 900 nm) laser fields. With such a field configuration, tuning of the relative phase between the ionizing, ω , and the perturbative, 2ω, field results in a modulation of the ionization rate, as well as modifications of the trajectories of electrons propagating in the laser-dressed continuum. Based on a semiclassical model, we confirm that phase dependencies, due to the perturbation of the ionization rate, encode the ionization times of the electrons. Here, using the fork structure, a well-known feature originating from well-defined dynamics allows us to distinguish between electrons ionized within distinct time windows. However, due to the simultaneous perturbation of the electron trajectories, the assignment of the ionization times can be distorted by up to 80 as, i.e., a 10° phase shift, which is independent of the degree of the perturbation.
R. Hollinger, D. Hoff, P. Wustelt, S. Skruszewicz, Y. Zhang, H. Kang, D. Würzler, T. Jungnickel, M. Dumergue, A. Nayak, R. Flender, L. Haizer, M. Kurucz, B. Kiss, S. Kuhn, E. Cormier, C. Spielmann, G.G. Paulus, P. Tzallas, and M. Kübel
Carrier-envelope-phase measurement of few-cycle mid-infrared laser pulses using high harmonic generation in ZnO
Opt. Express, 28 :7314 (March 2020)
High-harmonic generation (HHG) in crystals offers a simple, affordable and easily accessible route to carrier-envelope phase (CEP) measurements, which scales favorably towards longer wavelengths. We present measurements of HHG in ZnO using few-cycle pulses at 3.1 µm. Thanks to the broad bandwidth of the driving laser pulses, spectral overlap between adjacent harmonic orders is achieved. The resulting spectral interference pattern provides access to the relative harmonic phase, and hence, the CEP.
A. McIlvenny, H. Ahmed, C. Scullion, D. Doria, L. Romagnani, P. Martin, K. Naughton, A. Sgattoni, D. R. Symes, A. Macchi, P. McKenna, M. Zepf, S. Kar, and M. Borghes
Characteristics of ion beams generated inthe interaction of ultra-short laser pulseswith ultra-thin foils
Plasma Phys. Contr. F., 62 :054001 (March 2020)
Experiments investigating ion acceleration from laser-irradiated ultra-thin foils on the GEMINI laser facility at the Rutherford appleton laboratory indicate a transition to 'light sail' radiation pressure acceleration when using circularly polarised, high contrast laser pulses. This paper complements previously published results with additional data and modelling which provide information on the multispecies dynamics taking place during the acceleration, and provides an indication on expected scaling of these processes at higher laser intensities.
L. Klar
Detectable Optical Signatures of QED Vacuum Nonlinearities Using High-Intensity Laser Fields
Particles, 3 :223 (March 2020)
Up to date, quantum electrodynamics (QED) is the most precisely tested quantum field theory. Nevertheless, particularly in the high-intensity regime it predicts various phenomena that so far have not directly been accessible in all-optical experiments, such as photon-photon scattering phenomena induced by quantum vacuum fluctuations. Here, we focus on all-optical signatures of quantum vacuum effects accessible in the high-intensity regime of electromagnetic fields. We present an experimental setup giving rise to signal photons distinguishable from the background. This configuration is based on two optical pulsed petawatt lasers: one generates a narrow but high-intensity scattering center to be probed by the other one. We calculate the differential number of signal photons attainable with this field configuration analytically and compare it with the background of the driving laser beams.
R. Klas, W. Eschen, A. Kirsche, J. Rothhardt, and J. Limpert
Generation of coherent broadband high photon flux continua in the XUV with a sub-two-cycle fiber laser
Opt. Express, 28 :6188 (March 2020)
High harmonic sources can provide ultrashort pulses of coherent radiation in the XUV and X-ray spectral region. In this paper we utilize a sub-two-cycle femtosecond fiber laser to efficiently generate a broadband continuum of high-order harmonics between 70 eV and 120 eV. The average power delivered by this source ranges from > 0.2 µW/eV at 80 eV to >0.03 µW/eV at 120 eV. At 92 eV (13.5 nm wavelength), we measured a coherent record-high average power of 0.1 µW/eV, which corresponds to 7 · 109 ph/s/eV, with a long-term stability of 0.8% rms deviation over a 20 min time period. The presented approach is average power scalable and promises up to 1011 ph/s/eV in the near future. With additional carrier-envelop phase control even isolated attosecond pulses can be expected from such sources. The combination of high flux, high photon energy and ultrashort (sub-) fs duration will enable photon-hungry time-resolved and multidimensional studies.
Y. X. Zhang, S. Rykovanov, M. Shi, C. L. Zhong, X. T. He, B. Qiao, and M. Zepf
Giant Isolated Attosecond Pulses from Two-Color Laser-Plasma Interactions
Phys. Rev. Lett., 124 :114802 (March 2020)
A new regime in the interaction of a two-color (ω,2ω) laser with a nanometer-scale foil is identified, resulting in the emission of extremely intense, isolated attosecond pulses—even in the case of multicycle lasers. For foils irradiated by lasers exceeding the blow-out field strength (i.e., capable of fully separating electrons from the ion background), the addition of a second harmonic field results in the stabilization of the foil up to the blow-out intensity. This is then followed by a sharp transition to transparency that essentially occurs in a single optical cycle. During the transition cycle, a dense, nanometer-scale electron bunch is accelerated to relativistic velocities and emits a single, strong attosecond pulse with a peak intensity approaching that of the laser field.
C. Stihler, C. Jauregui, S. Kholaif, and J. Limpert
Intensity noise as a driver for transverse mode instability in fiber amplifiers
PhotoniX, 1 :2041 (March 2020)
The effect of transverse mode instability (TMI) is currently the main limitation for the further average-power scaling of fiber laser systems with diffraction-limited beam quality. In this work a main driving force for TMI in fiber amplifiers is identified. Our experiments and simulations illustrate that the performance of fiber laser systems in terms of their diffraction-limited output power can be significantly reduced when the pump or seed radiation exhibit intensity noise. This finding emphasizes the fact that the TMI threshold is not only determined by the active fiber but, rather, by the whole system. In the experiment an artificially applied pump intensity-noise of 2.9% led to a reduction of the TMI threshold of 63%, whereas a similar seed intensity-noise decreased it by just 13%. Thus, even though both noise sources have an impact on the TMI threshold, the pump intensity-noise can be considered as the main driver for TMI in saturated fiber amplifiers. Additionally, the work unveils that the physical origin of this behavior is linked to the noise transfer function in saturated fiber amplifiers. With the gained knowledge and the experimental and theoretical results, it can be concluded that a suppression of pump-noise frequencies below 20 kHz could strongly increase the TMI threshold in high-power fiber laser systems.
V. P. Kosheleva, A. V. Volotka, D. A. Glazov, and S. Fritzsche
Many-electron effects in the hyperfine splitting of lithiumlike ions
Phys. Rev. Research, 2 :013364 (March 2020)
The rigorous QED evaluation of the one- and two-photon exchange corrections to the ground-state hyperfine splitting in Li-like ions is presented for the wide range of nuclear charge number Z = 7-82. The calculations are carried out in the framework of the extended Furry picture, i.e., with the inclusion of the effective local screening potential in the zeroth-order approximation. The interelectronic-interaction contributions of the third and higher orders are taken into account in the framework of the Breit approximation employing the recursive perturbation theory. In comparison to the previous theoretical calculations, the accuracy of the interelectronic-interaction contributions to the ground-state hyperfine splitting in Li-like ions is substantially improved.
Y. Zhang, D. Zille, D. Hoff, P. Wustelt, D. Würzler, M. Möller, A. M. Sayler, and G. Paulus
Observing the Importance of the Phase-Volume Effect for Few-Cycle Light-Matter Interactions
Phys. Rev. Lett., 124 :133202 (March 2020)
The spatially dependent phase distribution of focused few-cycle pulses, i.e., the focal phase, is much more complex than the well-known Gouy phase of monochromatic beams. As the focal phase is imprinted on the carrier-envelope phase (CEP), for accurate modeling and interpretation of CEP-dependent few-cycle laser-matter interactions, both the coupled spatially dependent phase and intensity distributions must be taken into account. In this Letter, we demonstrate the significance of the focal phase effect via comparison of measurements and simulations of CEP-dependent photoelectron spectra. Moreover, we demonstrate the impact of this effect on few-cycle light-matter interactions as a function of their nonlinear intensity dependence to answer the general question: if, when, and how much should one be concerned about the focal phase?
B. Böning, W. Paufler, and S. Fritzsche
Polarization-dependent high-intensity Kapitza-Dirac effect in strong laser fields
Phys. Rev. A, 101 :031401 (March 2020)
We study the deflection of photoelectrons in intense elliptically polarized standing light waves, known as the high-intensity Kapitza-Dirac effect. In order to compute the longitudinal momentum transfer to the photoelectron in above-threshold ionization, we utilize a complete description of the quantum dynamics in the spatially dependent field of the standing light wave. We propose experimental conditions under which low-energy photoelectrons can be generated with remarkably high longitudinal momenta that can be controlled via the polarization of the standing wave. We expect that future experimental realizations will provide additional insights into the momentum transfer in intense laser-atom interactions.
Y. Ma, D. Seipt, A. E. Hussein, S. Hakimi, N. F. Beier, S. B. Hansen, J. Hinojosa, A. Maksimchuk, J. Nees, K. Krushelnick, A. G. R. Thomas, and F. Dollar
Polarization-Dependent Self-Injection by Above Threshold Ionization Heating in a Laser Wakefield Accelerator
Phys. Rev. Lett., 124 :114801 (March 2020)
We report on the experimental observation of a decreased self-injection threshold by using laser pulses with circular polarization in laser wakefield acceleration experiments in a nonpreformed plasma, compared to the usually employed linear polarization. A significantly higher electron beam charge was also observed for circular polarization compared to linear polarization over a wide range of parameters. Theoretical analysis and quasi-3D particle-in-cell simulations reveal that the self-injection and hence the laser wakefield acceleration is polarization dependent and indicate a different injection mechanism for circularly polarized laser pulses, originating from larger momentum gain by electrons during above threshold ionization. This enables electrons to meet the trapping condition more easily, and the resulting higher plasma temperature was confirmed via spectroscopy of the XUV plasma emission.
P. Balla, A. B. Wahid, I. Sytcevich, C. Guo, A.-L. Viotti, l. Silletti, A. Cartella, S. Ališauskas, H. Tavakol, U. Grosse-Wortmann, A. Schönberg, M. Seidel, A. Trabattoni, B. Manschwetus, T. Lang, F. Calegari, A. Couairon, A. LHuillier, C. Arnold, I. Hartl, and C. M. Heyl
Post-compression of picosecond pulses into the few-cycle regime
Opt. Lett., 45 :2572 (March 2020)
In this work, we demonstrate post-compression of 1.2 picosecond laser pulses to 13 fs via gas-based multipass spectral broadening. Our results yield a singlestage compression factor of about 40 at 200 W in-burst average power and a total compression factor >90 at reduced power. The employed scheme represents a route towards compact few-cycle sources driven by industrial-grade Yb:YAG lasers at high average power.
M. Afshari, J. Hornung, A. Kleinschmidt, P. Neumayer, D. Bertini, and V. Bagnoud
Proton acceleration via the TNSA mechanism using a smoothed laser focus
AIP Adv., 10 :035023 (March 2020)
In this work, we present the results of an experiment aiming at proton acceleration using a focus with a homogeneous intensity distribution, called smoothed focus. To achieve this goal, we implemented a phase plate before the pre-amplifier of the Petawatt High-Energy Laser for Heavy Ion EXperiments laser facility. The phase plate was used for the first time at a high-power short-pulse laser. Demonstrating a low divergent ion beam was the main goal of this work. Numerical simulations using the particle-in-cell code Extendable PIC Open Collaboration estimated a 2–5 times reduction in the angular divergence of the proton beam using a phase plate due to a smoother sheath at the rear side of the target. However, the reduction in the angular divergence was not sensible according to the experimental data. A positive point is that the spectrum of protons that are generated with the smoothed beam is shifted toward lower energies, provided that the laser absorption is kept in check, compared to the Gaussian proton spectrum. Moreover, the number of protons that are generated with the smoothed beam is higher than the ones generated with the Gaussian beam.