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In this paper we study the possibility of the space-charge compensation in the Fermilab Booster rapid cycling synchrotron with the use of several electron columns and show the significant promise of such technique.
All theories coupling electron emission theories ultimately approach the space-charge-limited current (SCLC) in vacuum, given by the Child–Langmuir (CL) law, for sufficiently high voltage, or the Mott–Gurney (MG) law for finite electron mobility and high (but not infinite) voltage. These analyses demonstrate the presence of an SCLC regime that cannot be described by either CL or MG. Here, we derive an exact solution for SCLC for general electron mobility and nonzero velocity. We recover the traditional CL with nonzero initial velocity at high voltage. For low mobility (or infinite collision frequency), we derive corrections to the MG law that depend on the ratio of initial velocity to the product of collision frequency and gap distance or initial velocity to drift velocity for low and high voltage, respectively. Increasing collisionality decreases the correction to SCLC for nonzero velocity, indicating that these corrections are less important for low-mobility materials (e.g., solids) than high-mobility materials (e.g., air or vacuum). For a given gap distance (collision frequency), increasing the collision frequency (gap distance) increases the voltage necessary to make the gap appear more like vacuum. These results provide a generalized SCLC for both collisionality and initial velocity when assessing the transitions between electron emission mechanisms.
Electron cooling as a method of creating intense ion beams has a practical upper limit when it comes to the peak phase space density of ion beams which can be achieved in practice. We describe a new experiment to study electron cooling of 2.5 MeV protons at the intensity limit using the Integrable Optics Test Accelerator (IOTA), which is a storage ring dedicated to beam physics research at Fermilab. This system will enable the study of magnetized electron cooling of a proton beam with transverse incoherent tune shifts approaching -0.5 due to the presence of intense space-charge forces. We present an overview of the hardware design, simulations and specific experiments planned for this project.
The Hofmann stability chart is used to screen working points in space-charge-dominated linacs. We identify two errors in its published higher-order dispersion relations: missing $(1\mp2\hatη^2/α)$ factors in the third-order $S^4$ coupling residues, and a sign error in the stated isotropic reduction of the fourth-order relation. Both corrections follow from Hofmann's Vlasov-Poisson equations without fitted parameters. They reproduce coherent tune-shift coefficients in the author's later monograph that the printed forms miss by 24% and 127%. Mode-resolved figures from a published application agree with the corrected relations and reject the printed forms, indicating an inconsistency between the 1998 equations and the calculations underlying those tested figures. We quantify the effect on the non-oscillatory stability chart. Inside the adopted $S^2\le10$ comparison domain, printed and corrected forms disagree on 0.73-2.11% of cells, with no preferred direction. Among excluded cells, disagreement reaches 22%, and the printed relation over-predicts instability at every sampled anisotropy. This concentration may help explain why the errors persisted, although it does not establish their historical cause. For PIP-II, the corrected chart flags four of thirty-two evaluable periods, including one on a third-order odd branch missed by a second-order screen. This count covers non-oscillatory modes only and remains conditional on an unresolved factor-five disagreement between two codes on transverse emittance growth.
Ionization profile monitors (IPMs) are widely used in accelerators for non-destructive and fast diagnostics of high energy particle beams. At high beam intensities, the space-charge forces make the measured IPM profiles significantly different from those of the beams. We analyze dynamics of the secondaries in IPMs and develop an effective algorithm to reconstruct the beam sizes from the measured IPM profiles. Efficiency of the developed theory is illustrated in application to the Fermilab 8 GeV proton Booster IPMs.
An interpretation of the unipolar figure of merit is formulated for wide bandgap (WBG) semiconductors based on the on-state specific resistance (RON,sp) derived from the space charge limited current–voltage relationship (Mott–Gurney square law). The limitations of the traditional Ohmic R ON,sp for WBG semiconductors are discussed, particularly at low doping, while the accuracy of the Mott–Gurney based R ON,sp is confirmed by Silvaco ATLAS drift–diffusion simulations of diamond Schottky pin diodes. The effects of incomplete ionization are considered as well.
Magnetized electron cooling is one of the major approaches towards obtaining the required high luminosity in the proposed Electron-Ion Collider (EIC). In order to increase the cooling efficiency, a bunched electron beam with a high bunch charge and high repetition rate is required. At Jefferson Lab, we generated magnetized electron beams with high bunch charge using a new compact DC high voltage photogun biased at -300 kV with bialkali-antimonide photocathode and a commercial ultra-fast laser. This contribution discusses how magnetization affects space charge dominated beams as a function of magnetic field strength, gun high voltage, and laser pulse width, and spot size in comparison with simulations performed using General Particle Tracer.
We report a new generation of gated x-ray detectors at the National Ignition Facility has brought faster, enhanced imaging capabilities. Their performance is currently limited by the amount of signal they can be operated with before space charge effects in their electron tube start to compromise their temporal and spatial response. We present a technique to characterize this phenomenon and apply it to a prototype of such systems, the Single Line Of Sight camera. Results of this characterization are used to benchmark Particle In Cell simulations of the electrons drifting inside the detector, which are found to well reproduce experimental data. These simulations are then employed to predict the optimum photon flux to the camera, with the goal to increase the quality of the images obtained on an experimental campaign while preventing the appearance of deleterious effects. They also offer some insight into some of the improvements that can be brought to the new pulse-dilation systems being built at Lawrence Livermore National Laboratory
We describe a new electron cooler being developed for 2.5 MeV protons at the Integrable Optics Test Accelerator (IOTA), which is a highly re-configurable storage ring at Fermilab. This system would enable the study of magnetized electron cooling in the presence of intense space-charge with transverse tune shifts approaching -0.5 as well as highly non-linear focusing optics in the IOTA ring. We present an overview of the design, simulations and hardware to be used for this project.
In recent EIC Coherent electron Cooling (CeC) design, we adopted 591 MHz SRF LINAC to accelerate electron beam to certain energy(150 MeV, 54.1 MeV and 22.3 MeV). To reduce the energy spread caused by the RF curvature, a short bunch is preferred and results in high peak current. The longitudinal space charge kick will cause the energy spread increasing and lengthen the bunch length when through the R56 elements. This slippage of modulated microbunches may misalign with hadrons providing imprinting at kicker section. In this note, we will estimate this effect and discuss possible solution.
Ionization profile monitors (IPMs) are widely used in accelerators for non-destructive and fast diagnostics of high energy particle beams. At low beam intensities, initial velocities of the secondaries to collect (ions or electrons) result in the IPM profile smearing. At high beam intensities, the space-charge forces make the measured IPM profiles significantly different from those of the beams. We analyze dynamics of the secondaries in IPMs, describe an effective algorithm to reconstruct the beam sizes from the measured IPM profiles and apply it to the Fermilab 8 GeV proton Booster and 70 MeV/c IOTA ring IPMs.
The Integrable Optics Test Accelerator (IOTA) at Fermilab is a small machine dedicated to a broad frontier accelerator physics program. An important aspect of this program is to investigate the potential benefits of the resonance free tune spread achievable with integrable optics to store and accelerate high intensity proton beams for which space charge is significant. In this context, a good understanding of proton beam emittance growth and particle loss mechanisms is essential. Assuming nominal design parameters, simulations show that for a bunched beam, the bulk of emittance growth takes place immediately following injection, typically within tens of turns. We attempt to account for this growth using a simplified RMS mismatch theory; some of its limitations and possible improvements are briefly discussed. We then compare theoretical predictions to simulations performed using the PIC code pyORBIT. Further exploring ways to mitigate emittance growth and reduce particle loss, we compare two beam matching strategies: (1) matching at the injection point (2) matching at the center of the nonlinear (octupole) insertion region where $\beta_x = \beta_y$. To observe how nonlinearity affects emittance growth and whether it dominates growth due to mismatch, we track two different distributions. Finally, we explore the potential of using octupoles in a quasi-integrable configuration to mitigate growth using a variety of initial distributions both at reduced and full intensities.
We show that trapped ions in virtual cathode potential wells can raise the transmitted current of emitted electrons into a plasma much closer to the full emission than is predicted by cathode sheath theories without trapped ions. The transmitted current is controlled by the well barrier voltage, which must adjust to balance the creation of low-energy ions within the well, and their loss. Our model considers the case of a plasma-facing cathode where trapped ions are created passively via charge-exchange collisions and lost passively via thermal leakage over the well. We quantify these rates and estimate the current in terms of system parameters for thermionic emission into a plasma with several cathode geometries. A general prediction is that the current as a function of emitted flux does not saturate at the traditional space charge limit (the onset of a well) but can reach far higher values until the trapped ion balance breaks down, causing instability. The maximum stable current depends on parameters but in principle can be arbitrarily high if active techniques are used to manipulate the trapped ion balance. We conclude that major improvements in plasma technologies with hot cathodes might be achieved by optimizing the current enhancement enabled by trapped ions.
Due to the fundamental limitations of scaling, very little progress has been made towards achieving a large-volume dense non-equilibrium plasma near atmospheric pressures. Commercially available state-of-the art glow-like atmospheric plasma devices for industrial applications are either narrow tubes or wide slits with narrow openings. Often multiple sources are put together in various configurations to process larger surfaces. The traditional methods of exciting electrodes create spatially fixed electric fields. As a result, the space charge at atmospheric pressure tends to be spatially confined resulting in non-uniformity which eventually leads to instability as the discharge is scaled. Theoretical work done under this project showed that it is possible to generate a spatially rotating electric field by exciting a set of electrodes with phase staggered sinusoidal waveforms. The modeling and simulations were done using plasma fluid models. It was shown that such a field can produce a uniform plasma. At the conclusion of the project, experimental proof of concept with an eight-electrode system in various gases (Air, Helium and Argon) was demonstrated. Power measurements and spectral investigation show that the concept can be used to generate a uniform stable plasma. This plasma source has the potential of opening new applications of nonthermal plasma including combustion of carbon-free fuel. The current limitation of the proposed method in scaling to higher volume and pressure is the need for multiple high voltage amplifiers.
The accumulation of very large ion populations in traveling wave (TW)-based Structures for Lossless ion Manipulations (SLIM) has been studied to better understand aspects of ‘in-SLIM’ ion accumulation, and particularly its use in conjunction with ion mobility spectrometry (IMS). A linear SLIM ion path was implemented that had a ‘gate’ for blocking and accumulating ions for arbitrary time periods. Removing the gate potential caused ions to exit and the spatial distributions of accumulated ions were examined. The ion populations for a set of peptides were observed to increase with increased accumulation times until space change effects became significant, after which the peptide precursor ion populations decreased due to growing space charge-related ion activation, reactions, and losses. Ions closest to the gate were preferentially activated, and increasingly so with added storage times, TW amplitude, and the size of the total ion population. For analytical applications, we found that relatively weak TWs in the accumulation/storage region should be utilized to prevent or minimize ion losses and/or ion heating effects that can also lead to fragmentation. Our results further indicate that an accumulation region close to the SLIM entrance is advantageous for both speeding accumulation, minimizing ion heating, and avoiding ion population profiles that result in IMS peak tailing. Importantly, space charge-driven separations were observed for large populations of accumulated species and attributed to the opposing effects of space charge and the TW. In these separations, ion species form distributions or peaks, sometimes moving against the TW, and ordered in the SLIM based on their mobilities. Such separations may offer utility for ion pre-fractionation of ions and increasing the dynamic range measurements, increasing the resolving power of IMS separations by decreasing peak widths for accumulated ion populations, and other purposes benefitting from separations of extremely large ion populations.
Further progress of fundamental physics requires accelerated beams of high intensity. The intensities, however, are limited by many factors, including coherent beam instabilities. Usual methods to control the instabilities, such as octupole magnets, beam feedback dampers and employment of chromatic effects, may be ineffective or insufficient. In this study, electron lenses were proposed as a means to provide stabilizing spread in the beam betatron frequencies. It was shown that electron lenses are uniquely effective for Landau damping of transverse beam instabilities in high energy particle accelerators, and that their employment does not compromise incoherent (single particle) stability, dynamic aperture and the beam lifetime. Here we consider effectiveness of the Landau damping with electron lenses when the space charge tune shift cannot be neglected. We demonstrate that the desired stability can be assured with proper choice of the electron beam parameters and current distributions.
The accumulation of positive ions, produced by ionizing particles crossing Liquid Argon Time Projection Chambers (LAr-TPCs), may generate distortions of the electric drift field affecting the track reconstruction of the ionizing events. These effects could become relevant for large LAr-TPCs operating at surface or at shallow depth, where the detectors are exposed to a copious flux of cosmic rays. We report a detailed study of such possible field distortions in the ICARUS T600 LAr-TPC has been performed analyzing a sample of cosmic muon tracks recorded with one T600 module operated at surface in 2001. The maximum track distortion turns out to be of few mm in good agreement with the prediction by a numerical calculation. As a cross-check, the same analysis has been performed on a cosmic muon sample recorded during the ICARUS T600 run at the LNGS underground laboratory, where the cosmic ray flux was suppressed by a factor $\sim 10^6$ by 3400 m water equivalent shielding. No appreciable distortion has been observed, confirming that the effects measured on surface are actually due to ion space charge.
Stark polarization spectroscopy is used to investigate the temporal evolution of the electric field distribution in the cathode region of a nanosecond pulsed discharge in helium at 120 Torr. The measurements are performed on the He I transition at 492.19 nm, during the early stages of the discharge formation. The experimental results are compared with the predictions of a 1D fluid model. Time-resolved ICCD images show that the discharge develops as a diffuse, cathode-directed ionization wave with a Townsend-like feature before transitioning into a glow-like structure. Near anode instabilities characterized by filament formation were observed near the high voltage electrode. Within 30 ns, a reduction of the sheath thickness to about 250 μm is observed, coinciding with a gradual increase of the discharge current and proportional increase in electric field at the cathode. Additionally, the cathode electric field corresponding to this sheath with a thickness of 250 μm is about 40 kV cm -1 . A subsequent steep increase of the discharge current leads to a further reduction of the sheath width. The electric field evolution as obtained by the fluid model is in excellent agreement with the measurements and shows that an enhanced ionization near the cathode is causing the space charge formation responsible for the increase in electric field.