Betatron Resonance Research Articles

Empirical condition of betatron resonances with space charge

This paper addresses the generalization of the single-particle betatron resonance condition derived by Courant and Snyder more than a half century ago. A two-dimensional resonance condition including the effect of space-charge interaction was recently conjectured from one-dimensional Vlasov predictions made by Sacherer, Okamoto, and Yokoya [K. Ito et al., Phys. Rev. Accel. Beams 20, 064201 (2017)]. The condition is remarkably simple which only contains a few measurable quantities and indicates the possibility that twice as many resonance stop bands as expected from the conventional incoherent picture may exist at high beam density. Self-consistent multiparticle simulations are performed systematically to locate low-order stop bands in the tune diagram. The proposed betatron resonance formula is shown to explain the basic feature of numerical observations, which suggests that no serious incoherent resonance is activated inside the phase-space core of a dense beam matched to the external linear focusing potential. It is confirmed that the coherent tune-shift factor of any collective mode is less than unity and practically considered as a constant over the whole tune space in a typical high-intensity storage ring. The procedure for finding the optimum operating point of the ring is discussed on the basis of the coherent picture instead of the commonly used picture relying on the concept of incoherent tune spread. Despite years of theoretical efforts by many researchers, the coherent resonance concept is still not being employed for the construction of a stability tune diagram. We here provide a simple prescription to draw the diagram quickly. The present study also indicates the possibility of complete suppression of emittance exchange on particular difference resonances by choosing a proper emittance ratio.

Space Charge studies on LEIR

The performance of the CERN Low Energy Ion Ring with electron cooled ion beams is presently limited by losses occurring once the beam has been captured in the RF buckets. An intense machine study program was started by the end of 2015 to mitigate the losses and improve the performance of the accelerator. The measurements pointed to the interplay of direct space charge forces and excited betatron resonances as the most plausible driving mechanism of these losses. In this paper, we present the systematic space-charge measurements performed in 2017 and compare them to space-charge tracking simulations based on an adaptive frozen potential.

Betatron resonance electron acceleration and generation of relativistic electron beams using 200 fs Ti:sapphire laser pulses

The generation of relativistic electron beams with quasi-thermal energy distribution (maximum energy: 30 MeV) by the interaction of a Ti:sapphire laser pulse of 200 fs duration, focussed to an intensity of ∼2.1 × 1018 W cm−2, with an underdense (electron density ∼3.6 × 1019 to ∼1.1 × 1020 cm−3) He gas-jet plasma was observed. We observed two stages of self-focusing of the laser pulse in the plasma. Two groups of accelerated electrons associated with these two stages of laser channeling were also observed, and are attributed to the betatron resonance acceleration mechanism. This is supported by 2D PIC simulations performed using the EPOCH code and a detailed theoretical analysis. Further, the generation of quasi-monoenergetic (ΔE/E ∼ 10%–20%) electron beams with a peak energy of ∼17–22 MeV was also observed, even with such long laser pulses, although with a low probability of occurrence.

Transverse electromagnetic Hermite–Gaussian mode-driven direct laser acceleration of electron under the influence of axial magnetic field

AbstractHermite–Gaussian (HG) laser beam with transverse electromagnetic (TEM) mode indices (m, n) of distinct values (0, 1), (0, 2), (0, 3), and (0, 4) has been analyzed theoretically for direct laser acceleration (DLA) of electron under the influence of an externally applied axial magnetic field. The propagation characteristics of a TEM HG beam in vacuum control the dynamics of electron during laser–electron interaction. The applied magnetic field strengthens the $\vec v \times \vec B$ force component of the fields acting on electron for the occurrence of strong betatron resonance. An axially confined enhanced acceleration is observed due to axial magnetic field. The electron energy gain is sensitive not only to mode indices of TEM HG laser beam but also to applied magnetic field. Higher energy gain in GeV range is seen with higher mode indices in the presence of applied magnetic field. The obtained results with distinct TEM modes would be helpful in the development of better table top accelerators of diverse needs.

Combined influence of azimuthal and axial magnetic fields on resonant electron acceleration in plasma

Resonant enhancement in electron acceleration due to a circularly polarized laser pulse in plasma, under the combined influence of external azimuthal and axial magnetic fields, is studied. We have investigated direct electron acceleration in plasma by employing a relativistic single particle simulation. The plasma is magnetized with an azimuthal magnetic field applied in the perpendicular plane and an axial magnetic field applied along the direction of laser beam propagation. Resonance takes place between electron and electric field of the laser pulse for the optimum value of the combined magnetic field, which supports electron acceleration to higher energies, up to the betatron resonance point. The optimum value of these magnetic fields is highly sensitive to laser initial intensity and laser initial spot size. The effects of laser intensity, initial spot size, and laser pulse duration are taken into consideration in optimizing the magnetic field for efficient electron acceleration. Higher electron energy gain, of the order of GeV, is observed by employing terawatt circularly polarized laser pulses in plasma under the influence of combined magnetic field of about 10 MG.

Producing ‘superponderomotive’ electrons in ashort cavitated channel

Particle-in-cell simulations suggest that a short cavitated channel in relativistic near-critical density plasma can be readily created by relativistic self-transparency and hole-boring effect. The strong self-generated magnetic fields confine the electrons in the plasma channel. Assisted by the magnetic fields, the electrons resonance with the laser fields at betatron resonance frequency . Consequently, highly energetic electrons with small divergence can be created by the betatron resonance regime. However, preliminary experiment results show higher temperature and larger divergence, compared to our simulation results. We argue that this difference would come from imperfect homogenization of foam target. Thus, the classical betatron resonance heating regime in a large scale of pre-plasma, which is proposed by Pukhov et al (1996 Phys. Rev. Lett. 76, 3975–8), would explain the experiment results instead.

Near-microcoulomb multi-MeV electrons generation in laser-driven self-formed plasma channel

AbstractThe origin and characteristics of near-microcoulomb multi-MeV electrons accelerated by short pulse lasers interacting with near-critical density plasma in self-formed channels are studied using three-dimensional particle-in-cell simulations. According to the analysis on interaction phenomena and electron dynamics, the dominant mechanism turns out to be direct laser acceleration, which ensures the outstanding energy coupling. Additionally, self-channeling is found to be a decisive factor for the acceleration performance, as electrons obtain ultra-high energy through betatron resonance inside the channels. In our findings, by using a relativistic short laser pulse and near-critical plasma, a large amount of energetic electrons can be generated, presenting a promising and accessible route to ultraintense, high-spatial-resolution radiation pulses.

High energetic electron bunches from lasernear critical density layer interaction

In this paper, we report our results from interactions between sub-picosecond laser and relativistic near-critical density plasma layer. To create the near-critical density plasma layer, low density foam targets are utilized in our experiments. The foam is comprised of tri-cellulose acetate. Their average densities vary from 1 mg/cm3 to 5 mg/cm3, corresponding to full ionization densities ranging from 0.6nc to 3nc. When laser pulse is incident on the near-critical density plasma, some energetic bunches with a large quantity of charges are measured in most of the shots. The maximum charge quantity reaches to 6.1 nC/sr. Furthermore, the observed electron energy spectrum is Boltzmann-like with a wide plateau at the tail of the energy spectrum, rather than a Maxwell-like. The concept of average temperature is not available any more, and we define average effective temperature instead, namely the slope temperature. Fitting the Boltzmann-like spectrum exponentially, we find that the average effective temperature even exceeds 8 MeV at 7.51019 W/cm2, far beyond the ponderomotive limit. Aiming at analyzing the implication of physics, several two-dimensional particle-in-cell (PIC) simulations are performed. The PIC simulations indicate that the hole-boring effect and relativistic self-transparency play an important role in the electrons heating process. At the earlier stage of heating process, a short plasma channel is created by the hole-boring effect and relativistic self-transparency. The length and the width of the plasma channel are about tens of micrometers and several micrometers respectively. Around the plasma channel, there is an intensive azimuthal magnetic field. The magnitude of the azimuthal magnetic field is 100 MGs. However, the radical electrostatic field is not seen. The possible reason is that the plasma channel would be cavitated by the hole-boring effect. As a result, the electrons will experience Betatron resonance in the magnetized plasma channel. The traverse momentum of the electron would be converted into forward momentum. Assisted by the Betatron resonance, the electrons gain energies from the laser directly and efficiently. Thus, the average effective temperatures of the electron bunches are much higher than predicted by the ponderomotive scaling law. Besides, we also conducte another simulation to instigate the differences by adopting different laser polarizations. Within our expectation, the electron spectrum of the P-polarization accords well with the experimental result, while the electron spectrum of the S-polarization obviously deviates from the experimental result. It also demonstrates that the Betatron resonance heating dominates the electron acceleration process. This research paves the way to generating the highly energetic bunches with a large quantity of charges, and wound also be helpful for producing the high-bright laser bremsstrahlung sources in future.

Double stop-band structure near half-integer tunes in high-intensity rings

Experiments at a table-top ion trap reveal space-charge driven coherent betatron resonances which will occur in high-intensity storage rings.

Resonantly Enhanced Betatron Hard X-rays from Ionization Injected Electrons in a Laser Plasma Accelerator.

Ultrafast betatron x-ray emission from electron oscillations in laser wakefield acceleration (LWFA) has been widely investigated as a promising source. Betatron x-rays are usually produced via self-injected electron beams, which are not controllable and are not optimized for x-ray yields. Here, we present a new method for bright hard x-ray emission via ionization injection from the K-shell electrons of nitrogen into the accelerating bucket. A total photon yield of 8 × 108/shot and 108 photons with energy greater than 110 keV is obtained. The yield is 10 times higher than that achieved with self-injection mode in helium under similar laser parameters. The simulation suggests that ionization-injected electrons are quickly accelerated to the driving laser region and are subsequently driven into betatron resonance. The present scheme enables the single-stage betatron radiation from LWFA to be extended to bright γ-ray radiation, which is beyond the capability of 3rd generation synchrotrons.

Multi-GeV electron acceleration by a periodic frequency chirped radially polarized laser pulse in vacuum

Linear and periodic effects of frequency chirp on electron acceleration by radially polarized (RP) laser pulse in vacuum have been investigated. A frequency chirp influences the electron dynamics, betatron resonance, and energy gain by electron during interaction with the RP laser pulse and ensures effective electron acceleration with high energy gain (~GeV). The electron energy gain with a periodic frequency chirped laser pulse is about twice as high as with a linear chirp. Our observations reveal electron energy gain of about 10.5 GeV with a periodic chirped RP petawatt laser pulse in vacuum.

Electron injection for direct acceleration to multi-GeV energy by a Gaussian laser field under the influence of axial magnetic field

Electron injected in the path of a circularly polarized Gaussian laser beam under the influence of an external axial magnetic field is shown to be accelerated with a several GeV of energy in vacuum. A small angle of injection δ with 0∘<δ<20∘ for a sideway injection of electron about the axis of propagation of laser pulse is suggested for better trapping of electron in laser field and stronger betatron resonance under the influence of axial magnetic field. Such an optimized electron injection with axial magnetic field maximizes the acceleration gradient and electron energy gain with low electron scattering.

Acceleration of electrons under the action of petawatt-class laser pulses onto foam targets

Optimization study for future experiments on interaction of petawatt laser pulses with foam targets was done by 3D PIC simulations. Densities in the range 0.5nc–nc and thicknesses in the range 100–500μm of the targets were considered corresponding to those which are currently available. It is shown that heating of electrons mainly occurs under the action of the ponderomotive force of a laser pulse in which amplitude increases up to three times because of self-focusing effect in underdense plasma. Accelerated electrons gain additional energy directly from the high-frequency laser field at the betatron resonance in the emerging plasma density channels. For thicker targets a higher number of electrons with higher energies are obtained. The narrowing of the angular distribution of electrons for thicker targets is explained by acceleration in multiple narrow filaments. Obtained energies of accelerated electrons can be approximated by Maxwell distribution with the temperature 8.5MeV. The charge carried by electrons with energies higher than 30MeV is about 30nC, that is 3–4 order of magnitude higher than the charge predicted by the ponderomotive scaling for the incident laser amplitude.

Beam loss caused by edge focusing of injection bump magnets and its mitigation in the 3-GeV rapid cycling synchrotron of the Japan Proton Accelerator Research Complex

In the 3-GeV rapid cycling synchrotron of the Japan Proton Accelerator Research Complex, transverse injection painting is utilized not only to suppress space-charge induced beam loss in the low energy region but also to mitigate foil scattering beam loss during charge-exchange injection. The space-charge induced beam loss is well minimized by the combination of modest transverse painting and full longitudinal painting. But, for sufficiently mitigating the foil scattering part of beam loss, the transverse painting area has to be further expanded. However, such a wide-ranging transverse painting had not been realized until recently due to beta function beating caused by edge focusing of pulsed injection bump magnets during injection. This beta function beating additionally excites random betatron resonances through a distortion of the lattice superperiodicity, and its resultant deterioration of the betatron motion stability causes significant extra beam loss when expanding the transverse painting area. To solve this issue, we newly installed pulse-type quadrupole correctors to compensate the beta function beating. This paper presents recent experimental results on this correction scheme for suppressing the extra beam loss, while discussing the beam loss and its mitigation mechanisms with the corresponding numerical simulations.

Electron injection for enhanced energy gain by a radially polarized laser pulse in vacuum in the presence of magnetic wiggler

We present a scheme of electron injection for enhanced electron energy gain by using a radially polarized (RP) laser pulse in vacuum under the influence of magnetic wiggler. The inherent symmetry of an RP laser pulse enforces the trapping and acceleration of electrons in the direction of propagation of laser pulse during laser electron interaction. A magnetic wiggler encircles the trajectory of accelerated electron and improves the strength of v→×B→ force which supports the retaining of betatron resonance for longer duration and leads to enhance electron acceleration. Four times higher electron energy is observed with a RP laser pulse of peak intensity 8.5×1020 W/cm2 in the presence of magnetic wiggler of 10.69 kG than that in the absence of magnetic wiggler. We have also analyzed the electron injection for enhanced energy gain and observe that the electron energy gain is relatively higher with a sideway injection than that of axial injection of electron. Injection angle δ is optimized and found that at δ=10° to the direction of propagation of laser pulse, maximum energy is obtained.

Sensitiveness of axial magnetic field on electron acceleration by a radially polarized laser pulse in vacuum

We examine the electron acceleration by a radially polarized (RP) laser pulse in vacuum under influence of an intense axial magnetic field. The electron while interaction with a RP laser pulse gets accelerated with high energy gain. The attained energy gain further enhanced up-to the order of GeV with an intense RP laser pulse. We observe a significant enhancement in energy gain in the presence of an intense axial magnetic field in the direction of propagation of laser pulse. The presence of axial magnetic field improves the strength of v→×B→ force which supports the retaining of betatron resonance for longer durations. This improves the electron acceleration with an enhanced energy gain up to 5.2GeV. It is noticed that the axial magnetic field is sensitive to electron acceleration, small change in magnetic field leads to enhance electron energy gain significantly. Our results also show relatively smaller scattering of the electrons in the presence of axial magnetic field.

Electron acceleration to GeV energy by a chirped laser pulse in vacuum in the presence of azimuthal magnetic field

Electron acceleration by a frequency-chirped circularly polarized (CP) laser pulse in vacuum in the presence of azimuthal magnetic field has been studied. A laser pulse propagating along +z-axis interacts with a pre-accelerated electron injected at a small angle in the direction of propagation of laser pulse in vacuum. The electron is accelerated with high energy in the presence of azimuthal magnetic field till the saturation of betatron resonance. A linear frequency chirp increases the duration of interaction of laser pulse with electron and hence enforces the resonance for longer duration. The presence of azimuthal magnetic field further improves the electron acceleration by keeping the electron motion parallel to the direction of propagation for longer distances. Thus, resonant enhancement appears due to the combined effect of chirped CP laser pulse and azimuthal magnetic field. An electron with few MeV of initial energy gains high energy of the order of GeV. Higher energy gain is obtained with intense chirped laser pulse in the presence of azimuthal magnetic field.

Numerical study for beam loss occurring for wide-ranging transverse injection painting and its mitigation scenario in the J-PARC 3-GeV RCS

In the J-PARC 3-GeV Rapid Cycling Synchrotron (RCS), transverse injection painting is utilized to manipulate the transverse beam profile according to the requirements from the downstream facilities as well as to mitigate the space-charge induced beam loss in RCS. Therefore, a flexible control is required for the transverse painting area. But now the available range of transverse painting is limited to small area due to beta function beating caused by the edge focus of injection bump magnets which operate during the beam injection period. This beta function beating additionally excites various random betatron resonances through a distortion of the lattice super-periodicity, causing a shrinkage of the dynamic aperture during the injection period. This decrease of the dynamic aperture leads to extra beam loss at present when applying large transverse painting. For beta function beating caused by the edge focus, we proposed a correction scheme with additional pulse-type quadrupole correctors. In this paper, we will discuss the feasibility and effectiveness of this correction scheme for expanding the transverse injection painting area with no extra beam loss, while considering the beam loss and its mitigation mechanisms, based on numerical simulations.

Electron acceleration in cavitated laser produced ion channels

This paper is concerned with the channeling of a relativistic laser pulse in an underdense plasma and with the subsequent generation of fast electrons in the cavitated ion channel. The laser pulse has a duration of several hundreds of femtoseconds and its power PL exceeds the critical power for laser channeling Pch, with Pch≈1.1Pc, Pc denoting the critical power for relativistic self-focusing. The laser pulse is focused in a plasma of electron density n0 such that the ratio n0/nc lies in the interval [10−3,10−1], nc denoting the critical density. The laser-plasma interaction under such conditions is investigated by means of three dimensional Particle-In-Cell (PIC) simulations. It is observed that the steep laser front gives rise to the excitation of a surface wave which propagates along the sharp radial boundaries of the electron free channel created by the laser pulse. The mechanism responsible for the generation of relativistic electrons observed in the PIC simulations is also analyzed by means of a test particles code. The fast electrons are found to be generated by the combination of a surface wave and of the betatron resonance. The maximum electron energy observed in the simulations is scaled as a function of PL/Pc; it reaches 350–600 MeV for PL/Pc = 70–140.

Generation of hemispherical fast electron waves in the presence of preplasma in ultraintense laser-matter interaction

AbstractHemispherical electron plasma waves generated from ultraintense laser interacting with a solid target having a subcritical preplasma is studied using particle-in-cell simulation. As the laser pulse propagates inside the preplasma, it becomes self-focused due to the response of the plasma electrons to the ponderomotive force. The electrons are mainly heated via betatron resonance absorption and their thermal energy can become higher than the ponderomotive energy. The hot electrons easily penetrate through the thin solid target and appear behind it as periodic hemispherical shell-like layers separated by the laser wavelength.