Self-modulation Process Research Articles

Устойчивые и неустойчивые динамические процессы в автоколебательной системе с тремя степенями свободы

The work is devoted to the study of the dynamic instability of coherent regimes of a system of two self-oscillators with a strong mutual resonant coupling. It is shown that this system can generate synchronous oscillations at three different frequencies, they correspond to the basic types of oscillations-modes: one in-phase and two anti-phase. A qualitative analysis of the influence of the characteristics of the resonant coupling on the stability of natural synchronous modes of oscillations has been carried out. An analytical criterion for the instability of in-phase oscillations and the conditions for its fulfillment are considered. The possibility of suppressing the stability of antiphase oscillations is discussed. The method of numerical simulation was used to study the temporal and spectral characteristics of oscillatory processes in various modes, including chaotic. Variants of the system behavior under competition and mode suppression accompanied by self-modulation processes are demonstrated. The features of dynamic chaos tuning and diagnostics of its components are discussed. The possibility of obtaining chaotic signals with a continuous spectrum in a band exceeding an octave is shown.

Analysis of proton bunch parameters in the AWAKE experiment

A precise characterization of the incoming proton bunch parameters is required to accurately simulate the self-modulation process in the Advanced Wakefield Experiment (AWAKE). This paper presents an analysis of the parameters of the incoming proton bunches used in the later stages of the AWAKE Run 1 data-taking period. The transverse structure of the bunch is observed at multiple positions along the beamline using scintillating or optical transition radiation screens. The parameters of a model that describes the bunch transverse dimensions and divergence are fitted to represent the observed data using Bayesian inference. The analysis is tested on simulated data and then applied to the experimental data.

Simulation and experimental study of proton bunch self-modulation in plasma with linear density gradients

We present numerical simulations and experimental results of the self-modulation of a long proton bunch in a plasma with linear density gradients along the beam path. Simulation results agree with the experimental results reported in arXiv:2007.14894v2: with negative gradients, the charge of the modulated bunch is lower than with positive gradients. In addition, the bunch modulation frequency varies with gradient. Simulation results show that dephasing of the wakefields with respect to the relativistic protons along the plasma is the main cause for the loss of charge. The study of the modulation frequency reveals details about the evolution of the self-modulation process along the plasma. In particular for negative gradients, the modulation frequency across time-resolved images of the bunch indicates the position along the plasma where protons leave the wakefields. Simulations and experimental results are in excellent agreement.

Theoretical and numerical studies of the phase velocity of wakefields in plasma driven by self-modulated proton beams with electron beam seeding

Significant progress has been made in the studies of wakefield excitation in plasma by a self-modulated high energy proton beam in the past decade. The electron beams accelerated up to 2 GeV by using such a wakefield were demonstrated in the AWAKE experiment at CERN in 2018. Aiming at the application of high energy particle accelerators, new ideas have been investigated in recent years, such as seeding the proton beam self-modulation with an electron beam in order to enhance the strength and stability of the wakefield or adding a density transition in the plasma distribution to enhance the phase velocity and the strength of the wakefield. Here in this work, we investigate the effects of electron beam seeding on the phase velocity of the wakefield generated by the modulated proton beam in plasma. The physical mechanisms responsible for the phase velocity change and the roles played by the electron beam seeding are discussed. The theoretical analysis and two-dimensional particle-in-cell simulations show that both the growth rate and the phase velocity of the wakefield generated by the modulated proton beam can be enhanced by the electron beam seeding. The higher the charge density of the electron beam, the more significant the enhancement effects. The effects of electron beam energy and proton beam longitudinal profiles on the increase of phase velocity are also studied. It is shown that the evolution of the electron beam distribution has a significant effect on the seeding self-modulation process, and thus affecting the phase velocity. A self-focusing electron seeding beam can increase the phase velocity of the wakefield even to superluminal while an expanding seeding beam can reduce the phase velocity and destroy the stability of the whole process. This work may benefit the proton beam seeding self-modulation acceleration and its applications.

Determination of the Charge per Micro-Bunch of a Self-Modulated Proton Bunch using a Streak Camera

The Advanced Wakefield Experiment (AWAKE) develops the first plasma wakefield accelerator with a high-energy proton bunch as driver. The 400 GeV bunch from CERN Super Proton Synchrotron (SPS) propagates through a 10 m long rubidium plasma, ionized by a 4TW laser pulse co-propagating with the proton bunch. The relativistic ionization front seeds a self-modulation process. The seeded self-modulation transforms the bunch into a train of micro-bunches resonantly driving wakefields. We measure the density modulation of the bunch, in time, with a streak camera with picosecond resolution. The observed effect corresponds to alternating focusing and defocusing fields. We present a procedure recovering the charge of the bunch from the experimental streak camera images containing the charge density. These studies are important to determine the charge per micro-bunch along the modulated proton bunch and to understand the wakefields driven by the modulated bunch.

Influence of the solenoid magnetic field on the self-modulation mechanism

For the guarantee of the long-distance transport of the bunches of China Initiative Accelerator Driven System (CIADS), a new scheme is proposed that extra magnetic field is used in the accelerator-target coupling section before the windowless target to minimize the self-modulation (SM) mechanism. Particle-in-cell simulations are carried out to study the influence of the solenoidal magnetic field on the self-modulation mechanism when long proton bunches move in the background plasmas. The long proton bunches used in the simulations are similar to these in the linear accelerator of CIADS. It is found that the presence of the solenoidal magnetic field will significantly inhibit the self-modulation process. For the strong magnetic field, the longitudinal separation and transverse focusing of the long bunches disappear. We attribute these phenomena to the reason that the strong solenoidal magnetic field restricts the transverse movement of plasma electrons. Thus, there are not enough electrons around the bunch to compensate the space charge effect. Moreover, without transverse current, the longitudinal pinched effect disappears, and the long bunch can not be separated into small pulses anymore.

Commissioning of the electron injector for the AWAKE experiment

The advanced wakefield experiment (AWAKE) at CERN is the first proton beam-driven plasma wakefield acceleration experiment. The main goal of AWAKE RUN 1 was to demonstrate seeded self-modulation (SSM) of the proton beam and electron witness beam acceleration in the plasma wakefield. For the AWAKE experiment, a 10-meter-long Rubidium-vapor cell together with a high-power laser for ionization was used to generate the plasma. The plasma wakefield is driven by a 400 GeV/c proton beam extracted from the super proton synchrotron (SPS), which undergoes a seeded self-modulation process in the plasma. The electron witness beam used to probe the wakefields is generated from an S-band RF photo-cathode gun and then accelerated by a booster structure up to energies between 16 and 20 MeV. The first run of the AWAKE experiment revealed that the maximum energy gain after the plasma cell is 2 GeV, and the SSM mechanism of the proton beam was verified. In this paper, we will present the details of the AWAKE electron injector. A comparison of the measured electron beam parameters, such as beam size, energy, and normalized emittance, with the simulation results was performed.

Phase-Stable Self-Modulation of an Electron Beam in a Magnetic Wiggler.

Electron beams with a sinusoidal energy modulation have the potential to emit subfemtosecond x-ray pulses in a free-electron laser. An energy modulation can be generated by overlapping a powerful infrared laser with an electron beam in a magnetic wiggler. We report on a new infrared source for this modulation, coherent radiation from the electron beam itself. In this self-modulation process, the current spike on the tail of the electron beam radiates coherently at the resonant wavelength of the wiggler, producing a six-period carrier-envelope-phase (CEP)-stable infrared field with gigawatt power. This field creates a few MeV, phase-stable modulation in the electron-beam core. The modulated electron beam is immediately useful for generating subfemtosecond x-ray pulses at any machine repetition rate, and the CEP-stable infrared field may find application as an experimental pump or timing diagnostic.

Acceleration of electrons in the interaction of a subterawatt laser pulse with a nonuniform plasma

We consider the effect of nonlinear self-focusing and self-modulation processes on the acceleration of electrons in the interaction of a subterawatt femtosecond laser pulse with a gas jet plasma. A three-dimensional particle-in-cell (3D PIC) simulation of the interaction of laser radiation with a low-density nonuniform plasma shows that laser pulse self-focusing that arises when the critical power of relativistic self-focusing determined by the local concentration of plasma electrons exceeds the pulse power results in efficient generation of a plasma wave. Due to a decrease in the phase velocity of the wake plasma wave generated via self-modulation of the laser pulse, electrons are trapped into the accelerating phase of the plasma wave and are accelerated to energies of ∼10 MeV. It is demonstrated that under the conditions for limiting the electrons’ acceleration region by the length of their dephasing, quasi-monoenergetic electron bunches with a characteristic energy of ∼9 MeV can be produced. The effective temperature of the accelerated electrons and their angular distribution, obtained by 3D PIC simulation, are in good agreement with those determined in the experiment.

Influence of proton bunch parameters on a proton-driven plasma wakefield acceleration experiment

We use particle-in-cell (PIC) simulations to study the effects of variations of the incoming 400 GeV proton bunch parameters on the amplitude and phase of the wakefields resulting from a seeded self-modulation (SSM) process. We find that these effects are largest during the growth of the SSM, i.e. over the first five to six meters of plasma with an electron density of $7 \times10^{14}$ cm$^{-3}$. However, for variations of any single parameter by $\pm$5%, effects after the SSM saturation point are small. In particular, the phase variations correspond to much less than a quarter wakefield period, making deterministic injection of electrons (or positrons) into the accelerating and focusing phase of the wakefields in principle possible. We use the wakefields from the simulations and a simple test electron model to estimate the same effects on the maximum final energies of electrons injected along the plasma, which are found to be below the initial variations of $\pm$5%. This analysis includes the dephasing of the electrons with respect to the wakefields that is expected during the growth of the SSM. Based on a PIC simulation, we also determine the injection position along the bunch and along the plasma leading to the largest energy gain. For the parameters taken here (ratio of peak beam density to plasma density $n_{b0}/n_0 \approx 0.003$), we find that the optimum position along the proton bunch is at $\xi \approx -1.5 \; \sigma_{zb}$, and that the optimal range for injection along the plasma (for a highest final energy of $\sim$1.6 GeV after 10 m) is 5-6 m.

Experimental Observation of Plasma Wakefield Growth Driven by the Seeded Self-Modulation of a Proton Bunch.

We measure the effects of transverse wakefields driven by a relativistic proton bunch in plasma with densities of 2.1×10^{14} and 7.7×10^{14} electrons/cm^{3}. We show that these wakefields periodically defocus the proton bunch itself, consistently with the development of the seeded self-modulation process. We show that the defocusing increases both along the bunch and along the plasma by using time resolved and time-integrated measurements of the proton bunch transverse distribution. We evaluate the transverse wakefield amplitudes and show that they exceed their seed value (<15 MV/m) and reach over 300 MV/m. All these results confirm the development of the seeded self-modulation process, a necessary condition for external injection of low energy and acceleration of electrons to multi-GeV energy levels.

A method to determine the maximum radius of defocused protons after self-modulation in AWAKE

The AWAKE experiment at CERN aims to drive GV/m plasma wakefields with a self-modulated proton drive bunch, and to use them for electron acceleration. During the self-modulation process, protons are defocused by the transverse plasma wakefields and form a halo around the focused bunch core. The two-screen setup integrated in AWAKE measures the transverse, time-integrated proton bunch distribution downstream the 10 m long plasma to detect defocused protons. By measuring the maximum radius of the defocused protons we attempt calculate properties of the self-modulation. In this article, we develop a routine to identify the maximum radius of the defocused protons, based on a standard contour method. We compare the maximum radius obtained from the contour to the logarithmic lineouts of the image to show that the determined radius identifies the edge of the distribution.

Application of the model of coupled oscillators in the analysis of the nonlinear excitation of hypersound in a ferrite plate under ferromagnetic resonance. Part 1. Basic equations

The excitation of hypersonic oscillations by ac magnetic field is considered in the framework of the problem of the magnetostriction microwave transducer using a model of coupled oscillators. Two regimes of the development of forced oscillations corresponding to an increase and decrease in the amplitude in time are separated by a bifurcation point. Two criteria of bifurcation are proposed to determine the critical values of the coupling constant and resonance frequency. The bifurcation point between the regimes is equivalent to the point of reorientation of the magnetization vector. It is demonstrated that the cubic nonlinearity plays the main role in the limitation of the exponential growth of the amplitude of forced oscillations. Frequency response functions (FRFs) of the coupled oscillations are considered at several excitation levels. It is demonstrated that the quadratic approximation provides the analysis of FRF with respect to magnetic oscillations with an accuracy of no worse than 2% if the ac-field amplitude is no greater than 0.7 of the saturation magnetization. The applicability of the quadratic approximation in the analysis of the self-sustained self-modulation process is considered. It is demonstrated that the model system fully characterizes the development of envelopes of both regular and chaotic self-modulation oscillations and the amplitude difference relative to the solution to the complete system is no greater than 20%. The calculations based on the model of coupled oscillators in the quadratic approximation allow a two-fold decrease in the computer resources and a decrease in the computation time by two orders of magnitude.

Electromagnetic radiation from laser wakefields in underdense plasma

AbstractIt is demonstrated by simulations and analysis that a wakefield driven by an ultrashort intense laser pulse in underdense plasma can emit tunable electromagnetic radiation along the laser propagation direction. The profile of such a kind of radiation is closely associated with the structure of the laser wakefield. In general, electromagnetic radiation in the terahertz range with its frequency a few times the electron plasma frequency can be generated in the moderate intensity regime. In the highly nonlinear case, a chain of radiation pulses is formed corresponding to the nonlinear structure of the wake. Study shows that the radiation is associated with the self-modulation process of the laser pulse in the wakefield and resulting transverse electron momenta from modulated asymmetric laser fields.

Numerical modeling of silicon evanescent lasers

A numerical self-consisted dynamic model of a silicon evanescent laser is presented. This model allows us to calculate the laser output power as a function of drive current and mode composition. Obtained results are in good agreement with published experimental data. Dynamic processes in silicon evanescent lasers are also investigated, and self-modulation processes are observed.

On the theory of self-modulation instability in an FEL amplifier due to stimulated scattering of counterpropagating waves

We present the results of numerical simulation of the self-modulation processes in an amplifier based on the effect of stimulated scattering of two counterpropagating transverse electromagnetic waves by a relativistic electron beam (FEL amplifier). Two models of the studied system are considered. One model allows for the effects of overbunching of electrons and is based on the modified method of macroparticles. The other is a simplified wave model obtained in the approximation that the amplitude of a combination wave is small if the nonlinearity of the electron-beam processes is negligibly small. The mechanisms of self-modulation are studied. The scenarios of transition to chaos, observed with increase in the input-signal intensity and system length, are examined.

Self-modulation of dipole-exchange magnetostatic waves in coupled ferromagnetic structure with perpendicular magnetization

The basic features of development of magnetostatic waves self-modulation processes in double-layer ferromagnetic structure are numerically studied in framework of system of the one-dimensional nonlinear nonstationary Schrodinger equations. The estimation of influence of coupling between films on group velocities, dispersion and nonlinearity coefficients was carried out taking into account the exchange interaction. The use of different types of excitations of coupled structure and change the value of coupling between films enables both to adjust frequency of MSW self-modulation, and to observe change of character of wave evolution in direction from order to chaos, and from chaos to order.

Self-modulation of light in piezoelectric crystals.

Spectroscopic measurements were used to monitor the optical interference of ordinary (o-ray) waves with extraordinary (e-ray) waves by incidence of plane-polarized light and transmission through piezoelectriccrystals (alpha-quartz, LiNbO3, and LiTaO3). This observation confirms that the rotations of the vibration planes of the o- and e-ray waves originate from the dynamic gratings induced by the electric field of the incident light. This is a self-modulation process of the polarized incident light in piezoelectric crystals.

Self-modulation processes and resulting generic 1/ f fluctuations

We analyze high precision data of transaction intervals in a foreign exchange market, and show that it is nicely approximated by a non-stationary Poisson process whose expectation value is given by a moving average of its own trace. Generalizing this result we introduce novel stochastic processes called the self-modulation processes. By the self-modulation effect, clustering occurs automatically resulting in fat-tailed interval distributions including the Zipf's law in an extreme case. We prove rigorously that the corresponding power spectrum follows the 1/ f spectrum.

Beams of magnetostatic backward volume waves at simultaneous developmentof self-modulation and self-focusing processes

The propagation of magnetostatic backward volume wave beams was numerically investigated using the nonlinear Schrodinger equation for а case of simultaneous manifestation of self-modulation and self—focusing effects. The conditions of non—conflict or mutually damping development of both self—action processes were found.