Space Charge Forces Research Articles

LEADS-DC: A computer code for intense dc beam nonlinear transport simulation

An intense dc beam nonlinear transport code has been developed. The code is written in Visual FORTRAN 6.6 and has ∼13000 lines. The particle distribution in the transverse cross section is uniform or Gaussian. The space charge forces are calculated by the PIC (particle in cell) scheme, and the effects of the applied fields on the particle motion are calculated with the Lie algebraic method through the third order approximation. Obviously, the solutions to the equations of particle motion are self-consistent. The results obtained from the theoretical analysis have been put in the computer code. Many optical beam elements are contained in the code. So, the code can simulate the intense dc particle motions in the beam transport lines, high voltage dc accelerators and ion implanters.

Charge resolved electrostatic diagnostic of colliding copper laser plasma plumes

The collision of two laser generated plasma plumes can result, under appropriate conditions, in the formation of a “stagnation layer.” The processes underlying this phenomenon are complex and time dependent. The majority of experiments over the last few decades have focused upon spectroscopic diagnostic of colliding plasmas. We have performed electrostatic diagnosis of multiply charged copper ions (Cu+ to Cu5+) generated via Q-switched pulsed laser (λ = 1.06 μm, τ = 6 ns, and EL = 52−525 mJ) generation of copper plasma plumes from a planar target. Time dependent current traces, charge yields, and kinetic energy (Ke) distributions are obtained for single plasma plumes (Sp) and colliding plasma plumes (Cp). The charge yield from a Cp relative to twice that from a Sp is characterized by a charge yield ratio (CYR) parameter. Superior ion yields for all charge states occur for a discrete range of fluences (F) from colliding plasma plumes leading to a CYR parameter exceeding unity. The kinetic energy distributions from colliding plasma plumes display well defined energy compression via narrowing of the distributions for all fluences and charge states. The extent of this energy compression is charge dependent. Space charge forces within the stagnation layer and the resulting charge dependent acceleration of ions are proposed to account for the transfer of ion kinetic energy in favour of collisional ionization mechanisms.

The IFMIF-EVEDA challenges in beam dynamics and their treatment

Abstract One major system of the IFMIF project (International Fusion Materials Irradiation Facility) is its two accelerators producing the neutron flux by accelerating deuteron particles up to 40 MeV against a lithium target. In the first phase called EVEDA (Engineering Validation and Engineering Design Activity), a full scale prototype accelerating particles up to 9 MeV is being studied and constructed in Europe, to be installed in Japan. Two unprecedented performances are required for the IFMIF-EVEDA accelerators: very high power of 5 MW and very high intensity of 125 mA CW. This leads to numerous unprecedented challenges in beam dynamics design and optimisation: harmful losses even for those less than 10−6 of the beam, non-linear dynamics induced by very strong space charge forces, difficulties for equipment and diagnostic implementations in the high compact structure, need of specific tuning strategies in this context. These issues are highlighted in this article, and the ways in which they are addressed are detailed.

Nonlinear Longitudinal Space Charge Oscillations in Relativistic Electron Beams

In this Letter we study the evolution of an initial periodic modulation in the temporal profile of a relativistic electron beam under the effect of longitudinal space-charge forces. Linear theory predicts a periodic exchange of the modulation between the density and the energy profiles at the beam plasma frequency. For large enough initial modulations, wave breaking occurs after 1/2 period of plasma oscillation leading to the formation of short current spikes. We confirm this effect by direct measurements on a ps-modulated electron beam from an rf photoinjector. These results are useful for the generation of intense electron pulse trains for advanced accelerator applications.

Bunch length measurement at Tsinghua Thomson scattering X-ray source

The length of electron beam from a photocathode RF gun is determined by a spectrometer, according to the relative energy spread induced by the bunch length during the acceleration in a linac. For a photocathode RF gun, different laser injected phase and beam charge are studied. The compression is changed for the different laser phases, as from 10° to 30°, and the bunch length is lengthened due to the strong longitudinal space charge force, caused by the increased charge.

Skin depth criterion for foil thickness in laser pressure acceleration of monoenergetic ions

An analytical formalism is developed to study the nonlinear laser penetration through radiation pressure accelerated thin foils, employed to produce high energy ions. We include the effects of relativistic mass increase and nonuniform electron density compression due to the ponderomotive force in plasma permittivity. For foils like diamond the usual optimum foil thickness lopt=λLncra0/πn0 (where λL and a0 are the wavelength and normalized amplitude of the laser), at which the ponderomotive force on electrons balances the space charge force due to the ions left behind, is significantly below the skin depth unless the laser intensity is excessively large and significant laser transmission through the foil reduces the radiation pressure on it. The reflection coefficient decreases with laser field strength, though the ponderomotive force led electron compression tends to raise it. The reflection coefficient also decreases significantly with foil velocity, which is a sensitive function of laser field strength and foil thickness.

Charged particle dynamics in a ‘high-pressure’ laser ion source

Charged particle sources require beam transport techniques specific to the application for optimum operation. The complexity of techniques increases as the degree of ionization and kinetic energy of charged particles increases. The Dublin City University laser ion source (DCU-LIS) utilizes a short field region (L = 48 mm) to maximize the average charge state and peak current extracted, thus ion extraction occurs at ‘high pressure’. The presence of large space-charge forces, high average plasma plume temperature and the expansion dynamics of laser-generated plasmas results in significant divergence of the ion bunch upon injection into the drift tube. To facilitate efficient beam transport, and to maximize system throughput, we employ a rather unique electrostatic transport system, termed as ‘continuous einzel array’ (CEA). Ion electrodynamics in such a system exhibit a number of distinct features which modify the system performance and alter the expected distribution of kinetic energies (KE), the times of flight and ion bunch diameters. System scalability in regard to beam kinetic energy is also important. In this paper the superior performance of the LIS equipped with a CEA is compared with a traditional einzel lens electrostatic beam transport system based on the usual 3-element and also a 5-element lens system.

Measurement of self-shaped ellipsoidal bunches from a photoinjector with postacceleration

Recent work has shown the possibility of generating self-shaped ellipsoidal beams with properties commensurate with the requirements of future light sources such as free-electron lasers and inverse Compton sources. In this so-termed ``blowout'' regime, short laser bunches are transformed via photoemission into short electron bunches which then self-consistently evolve into nearly uniform-density ellipsoids under space-charge forces. We report here on the first blowout studies conducted in collaboration between the UCLA Particle Beam Physics Lab and the Photo Injector Test Facility, Zeuthen (PITZ). The measurements conducted at the PITZ photoinjector facility examine the evolution of 750 pC, 2.7 ps FWHM electron bunches born in an L-band photoinjector and subsequently accelerated through a nine-cell L-band booster for a resulting energy of 12 MeV. These measurements represent the first observations of self-shaped ellipsoid evolution under postinjector acceleration, a key step in demonstrating the utility of such self-shaped beams at higher energy, where the advantages in both transverse and longitudinal and transverse phase space may be exploited in creating very high brightness beams.

Longitudinal confinement and matching of an intense electron beam

An induction cell has successfully been demonstrated to longitudinally confine a space-charge dominated bunch for over a thousand turns (>11.52 km) in the University of Maryland Electron Ring [Haber et al., Nucl. Instrum. Methods Phys. Res. A 606, 64 (2009) and R. A. Kishek et al., Int. J. Mod. Phys. A 22, 3838 (2007)]. With the use of synchronized periodic focusing fields, the beam is confined for multiple turns overcoming the longitudinal space-charge forces. Experimental results show that an optimum longitudinal match is obtained when the focusing frequency for containment of the 0.52 mA beam is applied at every fifth turn. Containment of the beam bunch is achievable at lower focusing frequencies, at the cost of a reduction in the transported charge from the lack of sufficient focusing. Containment is also obtainable, if the confinement fields overfocus the bunch, exciting multiple waves at the bunch ends, which propagate into the central region of the beam, distorting the overall constant current beam shape.

Self-Consistent expansion of a layer of electrons in the field of intrinsic space charge against the background of a neutral gas

The dynamics of self-consistent expansion of an electron layer under the action of the electric force of intrinsic space charge and friction force is investigated. The expansion of the electron layer occurs against the background of a neutral gas, which gives rise to the friction force opposing the motion of electrons. One-dimensional motion of electrons is considered for plane, cylindrical, and spherical symmetries. Exact analytic solutions are obtained to the linear system of hydrodynamic equations of plasma for electrons with a self-consistent electric field.

Microscopic kinetic analysis of space-charge induced optical microbunching in a relativistic electron beam

Longitudinal space-charge forces from density fluctuations generated by shot noise can be a major source of microbunching instability in relativistic high brightness electron beams. The gain in microbunching due to this effect is broadband, extending at least up to optical frequencies, where the induced structure on the beam distribution gives rise to effects such as coherent optical transition radiation. In the high-frequency regime, theoretical and computational analyses of microbunching formation require a full three-dimensional treatment. In this paper we address the problem of space-charge induced optical microbunching formation in the high-frequency limit when transverse thermal motion due to finite emittance is included for the first time. We derive an analytical description of this process based on the beam's plasma dielectric function. We discuss the effect of transverse temperature on the angular distribution of microbunching gain and its connection to the physics of Landau damping in longitudinal plasma oscillations. Application of the theory to a relevant experimental scenario is discussed. The analytical results obtained are then compared to the predictions arising from high resolution three-dimensional molecular dynamics simulations.

Multiplexed electrospray scaling for liquid fuel injection

Evaporation and space-charge requirements are evaluated to understand the effect of device scaling and fuel preheating for a liquid fuel injector using a multiplexed electrospray (MES) configuration in compact combustion applications. This work reveals the influence of the droplet diameter, droplet velocity and droplet surface temperature as well as the surrounding gas temperature on the size and performance of microfabricated MES. Measurements from MES devices are used in the model to accurately account for the droplet diameter versus flow rate relationship, the minimum droplet diameter and the relevant droplet velocities. A maximum extractor electrode to ground electrode distance of 3.1 mm required to overcome space-charge forces is found to be independent of voltage or droplet velocity for large levels of multiplexing. This maximum distance also becomes the required evaporation length scale which imposes minimum fuel pre-heating requirements for large flow densities. Required fuel preheating is therefore evaluated for both ethanol and 1-butanol with combustor parameters relevant to fuel reformation, thermoelectric conversion, thermophotovoltaic conversion and thermionic conversion.

Warp simulations for capture and control of laser-accelerated proton beams

The capture of laser-accelerated proton beams accompanied by co-moving electrons via a solenoid field has been studied with particle-in-cell simulations. The main advantages of the Warp simulation suite that we have used, relative to envelope or tracking codes, are the possibility of including all source parameters energy resolved, adding electrons as second species and considering the non-negligible space-charge forces and electrostatic self-fields. It was observed that the influence of the electrons is of vital importance. The magnetic effect on the electrons outbalances the space-charge force. Hence, the electrons are forced onto the beam axis and attract protons. Beside the energy dependent proton density increase on axis, the change in the particle spectrum is also important for future applications. Protons are accelerated/decelerated slightly, electrons highly. 2/3 of all electrons get lost directly at the source and 27% of all protons hit the inner wall of the solenoid.

The DCU laser ion source

Laser ion sources are used to generate and deliver highly charged ions of various masses and energies. We present details on the design and basic parameters of the DCU laser ion source (LIS). The theoretical aspects of a high voltage (HV) linear LIS are presented and the main issues surrounding laser-plasma formation, ion extraction and modeling of beam transport in relation to the operation of a LIS are detailed. A range of laser power densities (I approximately 10(8)-10(11) W cm(-2)) and fluences (F=0.1-3.9 kJ cm(-2)) from a Q-switched ruby laser (full-width half-maximum pulse duration approximately 35 ns, lambda=694 nm) were used to generate a copper plasma. In "basic operating mode," laser generated plasma ions are electrostatically accelerated using a dc HV bias (5-18 kV). A traditional einzel electrostatic lens system is utilized to transport and collimate the extracted ion beam for detection via a Faraday cup. Peak currents of up to I approximately 600 microA for Cu(+) to Cu(3+) ions were recorded. The maximum collected charge reached 94 pC (Cu(2+)). Hydrodynamic simulations and ion probe diagnostics were used to study the plasma plume within the extraction gap. The system measured performance and electrodynamic simulations indicated that the use of a short field-free (L=48 mm) region results in rapid expansion of the injected ion beam in the drift tube. This severely limits the efficiency of the electrostatic lens system and consequently the sources performance. Simulations of ion beam dynamics in a "continuous einzel array" were performed and experimentally verified to counter the strong space-charge force present in the ion beam which results from plasma extraction close to the target surface. Ion beam acceleration and injection thus occur at "high pressure." In "enhanced operating mode," peak currents of 3.26 mA (Cu(2+)) were recorded. The collected currents of more highly charged ions (Cu(4+)-Cu(6+)) increased considerably in this mode of operation.

Analytic model for the breakup of a coasting beam with space charge in isochronous accelerators

An analytical model based on the negative mass instability is introduced in this paper to explain the formation of the breakup of a coasting beam into small clusters in isochronous machines such as the case observed by Pozdeyev and Rodriguez in a small isochronous ring. Solving Poisson’s equation in both charge and vacuum regions with the longitudinal beam density perturbation, the coherent radial space charge force which decreases the transition gamma is obtained. It is found that the modified transition gamma depends on the wave number of the density perturbation, longitudinal beam density distribution, beam intensity, and beam size. By combining the longitudinal space charge force caused by the perturbation and the modified transition gamma, a dispersion relation for a monoenergetic beam is derived and evaluated for the fastest-growing instability mode in terms of the beam parameters, such as energy, bunch length, intensity, and emittance. The fastest-growing negative mass mode number, which determines not only the cluster number but also the growth rate of the instability, is proportional to the orbit radius and inversely proportional to the initial beam size. With the growth of the instability, the particles at the points of local minimum density move to the ones of local maximum density, with the transition gamma increasing. Since the growth rate depends on the longitudinal density distribution, therefore, instead of a constant growth rate, our model shows that the growth rate decreases with time. The results above can be applied to both short and long wavelength limits. As an important application of this theory, the beam breakup effect in the isochronous cyclotron CYCIAE-100 is predicted.

Electron dynamics simulations with Hellweg 2D code

In this paper Hellweg 2D code is introduced. It is a special tool for electron dynamics simulation in waveguide travelling wave accelerating structure. The underlying theory of this software is based on the differential equations of motion. The effects considered in this code include beam loading, space charge forces and external magnetic field. Hellweg 2D is capable of dealing with multisectional accelerators. Along with the analysis of electron linacs, this program is able to synthesize accelerating structures. This paper provides the comparison of the PARMELA, Hellweg 2D and experimental data of the existing facilities. The results of beam dynamics simulation in a hybrid accelerator with a standing wave (SW) buncher and travelling wave (TW) regular section are presented.

Numerical simulation for space charge dominated beam transport

To simulate the intense bunched beam transport, a computer program LEADS-3D has been developed. The particle trajectories are analysed with the Lie algebraic method. The third order approximation of the trajectory solutions is made with space charge forces off, and the second order approximation is made with space charge forces on. The particle distribution in the 3D ellipsoid is uniform or Gaussian. Most of the conventional beam optical elements are incorporated in the code. The optimization procedures are provided to fit the beam lines to satisfy the given optical conditions.

Transverse Schottky and beam transfer function measurements in space charge affected coasting ion beams

Transverse Schottky spectra and beam transfer functions (BTFs) of coasting ion beams were measured in the heavy ion synchrotron SIS-18 in order to study the impact of space charge on the transverse beam dynamics. The particle number in the beam was varied to investigate the intensity dependence of the space-charge effect. No cooling was applied to the beams throughout the experiment. The expected deformation of the Schottky spectra and BTFs is observed. An analytic model with linear space charge is employed to describe the deformed Schottky and BTF signals. In this model, the incoherent space-charge force and the coherent forces due to impedances are treated separately. Using the model, the space-charge induced tune shift is evaluated both from the position and the form of the signals. The data are well described by the model, only in the high-intensity BTFs deviations are observed. The stability diagrams are shifted according to the space-charge parameter obtained from the BTFs. In addition, the tune shift is estimated by virtue of measured beam profiles and particle numbers. The estimated tune shift is of the same order of magnitude but smaller than the measured one. Possible explanations for deviations between the measurements, the model, and the estimation are discussed.

Research on feasibility of closed and offset PCM focusing structures for sheet electron beams

Using theoretical analysis and numerical calculation, it has been demonstrated that the closed periodic cusped magnetic （PCM） field can effectively confine the sheet electron beam in two transverse directions simultaneously to realize the stable long distance transport, where the beam cross-section has an attainable shape of the state of the art. Moreover, the method for matching the transverse magnetic focusing force and the inner space charge force in the wide dimension of the sheet beam is given, which can be used to determine the longitudinal periodic length and the cross section shape of the closed PCM structure. The calculation has also shown that the optimum focusing can be acquired through adjusting the width of the closed PCM structure independently. And besides, it has been proven that the offset PCM structure is not a good choice for sheet beams’ confinement. The work presented in the paper indicates that the closed PCM structure is very promising, and it’s helpful for guiding the practical engineering design.

Validity of closed periodic magnetic focusing for sheet electron beams

Theoretical analyses and numerical calculations have demonstrated that a closed periodic cusped magnetic (PCM) field can effectively confine a sheet electron beam in two transverse directions (i.e., in the wide and narrow dimensions, simultaneously) for stable long distance transport in which the sizes of the beam cross section are set by referring to the present state of the art. Moreover, the method for matching the transverse magnetic focusing force and the inner space charge force in the wide dimension of the sheet electron beam is given, and the longitudinal periodic length and the cross sectional shape of the closed PCM focusing structure can be determined. Calculations also demonstrate that the optimum focusing state can be attained by adjusting the wide dimension on the transverse section of the closed PCM structure independently. The work presented in this paper indicates that the closed PCM structure is very promising for the confinement of the sheet electron beam, and it can be helpful for guiding practical engineering design.