Nonlinear Space Charge Forces Research Articles

Widely tunable electron bunch trains for the generation of high-power narrowband 1–10 THz radiation

Terahertz radiation enables the coherent excitation of many fundamental modes, such as molecular rotation, lattice vibration and spin precession. To excite the transient state of matter far out of equilibrium, high-power and tunable narrowband terahertz radiation sources have been in great demand for years. However, the terahertz source available at present cannot meet these tunability and power demands, leaving a large scientific gap that has yet to be fully explored. Here we convert the energy modulation induced by the nonlinear longitudinal space charge force to a density modulation and experimentally demonstrate the generation of electron bunch trains with modulation frequencies that are adjustable between 1 and 10 THz. The electron bunch trains can be directly used to produce tunable high-power narrowband terahertz radiation that fully covers the long-standing ‘terahertz gap’, which will open up many more possibilities in terahertz science. A tunable terahertz radiation pulse is demonstrated based on a linear accelerator. The emission frequency of this terahertz radiation is tunable from 1 to 10 THz by changing the bunching frequency of a 34 MeV electron beam. The pulse energy is at the submillijoule level.

Analysis of slice transverse emittance evolution in a very-high-frequency gun photoinjector

Emittance is a key figure-of-merit for high brightness electron beams that enable the success of a broad range of modern accelerator-based instruments. With the successful implementation of the emittance compensation scheme and beam-shaping techniques to align each temporal beam slice in phase space, slice emittance starts to play a more dominating role in determining the beam quality. In this paper, we develop an approach, combining simulations and analytical calculations, to systematically study the evolution of the slice emittance in a very high frequency gun photoinjector, which is under intense R worldwide for driving the next generation continuous-wave accelerators. Our approach is capable of tracing various sources that introduce curvature in the transverse phase space, corresponding to the growth of the slice emittance. It is shown that nonlinear transverse space charge forces in the vicinity of cathodes and the spherical aberration of the focusing solenoid are the main sources of nonlinear forces, while in a long drift section space charge forces can actually compensate for nonlinear transverse position-momentum correlations and hence recover the emittance. We further demonstrate that the sources of nonlinearities can be controlled by tailoring the transverse beam density profile and the design of solenoid lenses.

Rapid charge redistribution leading to core hollowing in a high-intensity ion beam

Recently, the first direct measurement of a full 6D accelerator beam distribution was reported [1]. That work observed a correlation between energy and transverse coordinates, for which the energy distribution becomes hollowed and double-peaked near the transverse core. In this article, a similar structure is shown to emerge in expansion of an initially uncorrelated, high density bunched beam as the result of velocity perturbation from nonlinear space charge forces. This hollowing is obscured when the 6D phase space is projected onto one- and two-dimensional axes. This phenomenon has not been widely recognized in accelerator systems, but parallels can be drawn to observations of laser-ionized nanoclusters and electron sources for diffraction. While this effect provides insight into the origin of the measured core correlation, it does not provide a complete description. A better reproduction of the measured structure can be obtained via self-consistent simulation through the radio-frequency quadrupole. [1] B. Cathey, S. Cousineau, A. Aleksandrov, and A. Zhukov, PRL 121, 064804 (2018).

Envelope dynamics and stability with non-linear space-charge forces

We developed a model to calculate the stability of Gaussian beam distributions with non-linear space-charge forces in the presence of random and skew-quadrupole errors. The effect of the space-charge force on the beam matrix is calculated analytically including full cross-plane coupling in 4D phase space, which allows us to perform fast parameter studies. For stability analysis, we find the fixed points of the beam including the space-charge forces and construct a Jacobi-matrix by slightly perturbing the periodic solution. The stability of envelope oscillations is inferred by eigenvalue analysis. Furthermore, we employ envelope tracking as a complementary method and compare the results of the eigenvalue analysis with FFT data from the tracked envelope. The non-linearity of the space-charge force in combination with lattice errors and beam coupling opens up for envelope-lattice resonances and envelope coupling resonances. Hitting these resonances leads to envelope blow-up, causing an effective beam mismatch. Therefore, we finally examine the effect of beam mismatch on the envelope tune-shift and its stability.

A study of coherent and incoherent resonances in high intensity beams using a linear Paul trap

In this paper we present the first quantitative measurement of the change in frequency (tune) with intensity of four transverse resonances in a high intensity Gaussian beam. Due to the nonlinear space charge forces present in high intensity beams, particle motion cannot be analytically described. Instead we use the simulator of particle orbit dynamics and the intense beam experiment, two linear Paul traps (LPTs), to replicate the system experimentally. In high intensity beams a coherent resonant response to both space charge and external field driven perturbations is possible, these coherent resonances are excited at a tune that differs by a factor Cm from that of the incoherent resonance. By increasing the number of ions stored in the LPT and studying the location of four different resonances we extract provisional values describing the change in tune of the resonance with intensity. These values are then compared to the Cm factors for coherent resonances. We find that the Cm factors do not accurately predict the location of resonances in high intensity Gaussian beams. Further insight into the experiment was gained through simulation using Warp, a particle-in-cell code.

Suppression of beam halo in an RF linac using a hollow electron beam

AbstractHigh-intensity electron linacs have severe space-charge effects that lead to the production of beam halo which degrade the beam quality. For a given charge per bunch, hollow beams have a weaker nonlinear space-charge force. In this paper, we have investigated the possibility of using hollow beam to control halo growth in linacs. We simulate the dynamics of such a beam in a 17 MeV radio frequency linac using ASTRA beam dynamics code and show that it experiences a smaller emittance growth as well as reduced beam halo. The results suggest that using a hollow beam, high charge per bunch could be propagated and accelerated in a radio frequency linac.

Higher order mode beams mitigate halos in high intensity proton linacs

High intensity proton linacs (HIPLs) for applications such as Accelerator Driven Reactor Systems (ADRS) have serious beam dynamics issues related to beam halo formation. This can lead to particle loss and radioactivation of the surroundings which consequently limit the beam current. Beam halos are largely driven by the nonlinear space-charge force of the beam, which depends strongly on the beam distribution and also on the initial beam mismatch. We propose here the use of a higher order mode beam (HOMB), that has a weaker nonlinear force, to mitigate beam halos. We first show how the nonlinear space-charge force can itself be exploited in the presence of nonlinear solenoid fields, to produce a HOMB in the low energy beam transport (LEBT) line. We then study the transport of such a beam through a radio frequency quadrupole (RFQ), and show that the HOMB has a significant advantage in terms of emittance blow-up, halo formation and beam loss, over a Gaussian beam, even with a finite initial mismatch. For example, for the transport of a 30 mA beam through the RFQ, with an initial beam mismatch of 45%, the Gaussian beam sees an emittance blow-up of 125%, while the HOMB sees a blow-up of only 35% (relative to the initial emittance of $0.2\ensuremath{\pi}\text{ }\text{ }\mathrm{mm}\text{\ensuremath{-}}\mathrm{mrad}$). Similarly, the beam halo parameter and beam loss are 0.95 and 25% respectively for a Gaussian beam, but only 0.35 and 15% for a HOMB. The beam dynamics of the HOMB agrees quite well with the particle-core model, because of the more linear space-charge force, while for the Gaussian beam there are additional particle loss mechanisms arising from nonlinear resonances. Therefore, the HOMB suppresses emittance blow-up and halo formation, and can make high current ADRS systems more viable.

Suppression of space charge induced beam halo in nonlinear focusing channel

An intense non-uniform particle beam exhibits strong emittance growth and halo formation in focusing channels due to nonlinear space charge forces of the beam. This phenomenon limits beam brightness and results in particle losses. The problem is connected with irreversible distortion of phase space volume of the beam in conventional focusing structures due to filamentation in phase space. Emittance growth is accompanied by halo formation in real space, which results in inevitable particle losses. A new approach for solving a self-consistent problem for a matched non-uniform beam in two-dimensional geometry is discussed. The resulting solution is applied to the problem of beam transport, while avoiding emittance growth and halo formation by the use of nonlinear focusing field. Conservation of a beam distribution function is demonstrated analytically and by particle-in-cell simulation for a beam with a realistic beam distribution.

Analysis of transverse RMS emittance growth of a beam induced by spherical and chromatic aberration in a solenoidal field

In a medium energy beam transport line transverse rms emittance growth associated with spherical aberration is analysed. An analytical expression is derived for beam optics in a solenoid field considering terms up to the third order in the radial displacement. Two important phenomena: effect of spherical aberrations in axial-symmetric focusing lens and influence of nonlinear space charge forces on beam emittance growth are discussed for different beam distributions. In the second part nonlinear effect associated with chromatic aberration that describes the growth of emittance and distortion of phase space area is discussed.

Dynamics of intense particle beam in axial-symmetric magnetic field

Axial-symmetric magnetic field is often used in focusing of particle beams. Most existing ion Low Energy Beam Transport lines are based on solenoid focusing. Modern accelerator projects utilize superconducting solenoids in combination with superconducting accelerating cavities for acceleration of high-intensity particle beams. Present article discusses conditions for matched beam in axial-symmetric magnetic field. Analysis allows us to minimize power consumption of solenoids and beam emittance growth due to nonlinear space charge, lens aberrations, and maximize acceptance of the channel. Expressions for maximum beam current in focusing structure, beam emittance growth due to spherical aberrations and non-linear space charge forces are derived.

Design of low energy beam transport for new LANSCE H+ injector

The present LANSCE injector utilizes two 750-keV Cockcroft–Walton (CW) based injectors for simultaneous injection of H+ and H− beams into 800-MeV accelerator. To reduce long-term operational risks, the new project to replace the existing H+ CW injector with a Radio-Frequency Quadrupole (RFQ) accelerator is underway [1]. The new injector requires a Low-Energy Beam Transport (LEBT). An ion source and 2-solenoid magnetic LEBT have been designed and optimized to transport beams over a wide range of space-charge neutralization and transverse emittance, while allowing sufficient space for diagnostics and a beam deflector. The design layout minimizes the beam size in the LEBT and potential emittance growth due to solenoid aberrations and nonlinear space-charge forces. This paper describes the details of the LEBT design activity.

Phase-Space Dynamics of Ionization Injection in Plasma-Based Accelerators

The evolution of beam phase space in ionization injection into plasma wakefields is studied using theory and particle-in-cell simulations. The injection process involves both longitudinal and transverse phase mixing, leading initially to a rapid emittance growth followed by oscillation, decay, and a slow growth to saturation. An analytic theory for this evolution is presented and verified through particle-in-cell simulations. This theory includes the effects of injection distance (time), acceleration distance, wakefield structure, and nonlinear space charge forces, and it also shows how ultralow emittance beams can be produced using ionization injection methods.

Controlling nonlinear longitudinal space charge oscillations for high peak current bunch train generation

The evolution of picosecond modulations of the longitudinal profile of an electron beam generated in an rf photoinjector is analyzed and optimized with the goal of obtaining high peak current electron bunch trains at very high frequencies ($\ensuremath{\ge}\mathrm{THz}$). Taking advantage of nonlinear longitudinal space charge forces, it is found that more than 500 A peak current 1 THz bunch trains can be generated using a standard 1.6 cell SLAC/UCLA/BNL rf gun. Postacceleration is used to freeze the longitudinal phase space dynamics after one half plasma oscillation. Applications range from tunable narrow bandwidth THz radiation generation to drivers for high frequency high gradient accelerators.

Studies of space-charge-dominated multispecies beam in a solenoid based beam transport line

A self-consistent particle-in-cell (PIC) simulation is used to study the transport properties of a space-charge-dominated multispecies beam propagating through a solenoid-based low energy beam transport line. The evolution of the beam radius and emittance growth of each species arising due to the nonlinear space-charge forces has been investigated. The self-consistent PIC simulation shows the formation of hollow density profiles of subdominant unwanted species around the primary beam, downstream of the transport line. We have utilized this effect for efficient removal of unwanted species by making use of a slit at a suitable location in the beam line.

Advanced Laser Technologies for High-brightness Photocathode Electron Gun

A laser-excited photocathode RF gun is one of the most reliable high-brightness electron beam sources for XFELs. Several 3D laser shaping methods have been developed as ideal photocathode illumination sources at SPring-8 since 2001. To suppress the emittance growth caused by nonlinear space-charge forces, the 3D cylindrical UV-pulse was optimized spatially as a flattop and temporally as squarely stacked chirped pulses. This shaping system is a serial combination of a deformable mirror that adaptively shapes the spatial profile with a genetic algorithm and a UV-pulse stacker that consists of four birefringent α-BBO crystal rods for temporal shaping. Using this 3D-shaped pulse, a normalized emittance of 1.4 π mm mrad was obtained in 2006. Utilizing laser's Z-polarization, Schottky-effect-gated photocathode gun was proposed in 2006. The cathode work functions are reduced by a laser-induced Schottky effect. As a result of focusing a radially polarized laser pulse with a hollow lens in vacuum, the Z-field (Z-polarization) is generated at the cathode.

Stability of transverse dipole modes in coasting ion beams with nonlinear space charge, octupoles, and chromaticity

The influence of the nonlinear space-charge force, which causes an amplitude-dependent tune shift, on the transverse stability of a coasting beam with impedances is investigated. In particular, the interplay of nonlinear space charge with a cubic lattice nonlinearity (octupoles) and with linear chromatic effects is considered. For each case, the stability diagram obtained from a dispersion relation with two-dimensional tune spread is compared with results from a simulation scan. For the latter, a 3D particle tracking code is used, with self-consistent 2D space charge, coupling to transverse impedances, chromaticity, and nonlinear lattice effects. The validity of non-self-consistent space-charge models in analytical and in numerical approaches is examined. We reconfirm that, although nonlinear space charge does not provide Landau damping of its own, it modifies strongly the stability properties and must be taken into account in an analysis of Landau damping induced by external (octupole or chromaticity) effects. It is demonstrated that non-self-consistent approaches for space charge are not always applicable.

DESIGN OF A 2 kA, 30 fs RF-PHOTOINJECTOR FOR WATERBAG COMPRESSION

Because uniformly filled ellipsoidal ‘waterbag’ bunches have linear self-fields in all dimensions, they do not suffer from space-charge induced brightness degradation. This in turn allows very efficient longitudinal compression of high-brightness bunches at sub or mildly relativistic energies, a parameter regime inaccessible up to now due to detrimental effects of non-linear space-charge forces. To demonstrate the feasibility of this approach, we investigate ballistic bunching of 1 MeV, 100 pC waterbag electron bunches, created in a half-cell rf-photogun, by means of a two-cell booster-compressor. Detailed GPT simulations of this table-top set-up are presented, including realistic fields, 3D space-charge effects, path-length differences and image charges at the cathode. It is shown that with a single 10MW S-band klystron and fields of 100 MV/m, 2kA peak current is attainable with a pulse duration of only 30 fs at a transverse normalized emittance of 1.5 μm.

Space charge compensation studies of hydrogen ion beams in a drift section

Demands of high intensity beams are increasing for material science and engineering applications. To control the high intensity beam dynamics, the nonlinear space charge forces, produced by the beam and the residual plasma at low energy, have to be carefully studied. Interactions between the beam and the residual gas tend to neutralize the beam space charge. The temporal and spatial evolutions of these interactions complicate the beam dynamics, even into a drift section. A 1.5D ($xy$ for motion, $r$ for space charge) PIC code, CARTAGO, has been written in order to simulate the beam dynamics in a low energy beam transport line including the space charge compensation effects. This paper relates the structure and the numerical methods used in the code and shows studies of the space charge compensation regime for ${\mathrm{H}}^{+}$ and ${\mathrm{H}}^{\ensuremath{-}}$ beams in a drift section.

Nonlinearδfparticle simulations of collective excitations and energy-anisotropy instabilities in high-intensity bunched beams

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov-Maxwell equations are applied to high-intensity finite-length charge bunches, and a generalized particle simulation algorithm is developed for bunched beams with or without energy anisotropy. The nonlinear method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out under conditions corresponding to strong 3D nonlinear space-charge forces in the beam frame. For charge bunches with isotropic energy, finite bunch-length effects are clearly evident by the fact that the spectra for an infinitely long coasting beam and a nearly spherical charge bunch have strong similarities, whereas the spectra have distinctly different features when the bunch length is varied between these two limiting cases. For bunched beams with anisotropic energy, there exists no exact kinetic equilibrium because the particle dynamics do not conserve transverse energy and longitudinal energy separately. A reference state in approximate dynamic equilibrium has been constructed theoretically, and a quasi-steady state has been established in the simulations for the anisotropic case. Collective excitations relative to the reference state have been simulated using the generalized algorithm. In particular, the electrostatic Harris instability driven by strong energy anisotropy is investigated for a finite-length charge bunch. The observed growth rates are larger than those obtained for infinitely long coasting beams. However, the growth rate decreases for increasing bunch length to a value similar to the case of a long coasting beam. For long bunches, the instability is axially localized symmetrically relative to the beam center, and the characteristic wavelength in the longitudinal direction is comparable to the transverse dimension of the beam.

Nonlinear [formula omitted] particle simulations of collective effects in high-intensity bunched beams

Collective effects with strong coupling between the longitudinal and transverse dynamics are of fundamental importance for applications of high-intensity bunched beams. The self-consistent Vlasov–Maxwell equations are applied to high-intensity bunched beams, and a generalized δ f particle simulation algorithm is developed for bunched beams with or without energy anisotropy. Numerically, the distribution function is spit into a reference distribution and a perturbed part. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by the equations of motion in the focusing field and self-generated fields, and the particle weights are advanced by an equation equivalent to the nonlinear Vlasov equation. The nonlinear δ f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. Systematic studies are carried out for the particle dynamics under conditions corresponding to strong 3D nonlinear space-charge force. The simulations showed that finite bunch-length effects on the collective excitations become insignificant when the aspect ratio ( z b / r b ) is larger than 10 for a moderately intense beam with normalized intensity s b = ω p b 2 / 2 ω β 2 = 0.27 . For bunched beams with energy anisotropy ( T ∥ / T ⊥ < 1 ) , a reference state has been constructed and a dynamic equilibrium is established in the simulations. Collective excitations relative to the dynamic equilibrium have also been successfully simulated by the generalized δ f algorithm.