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Recent studies indicate better efficacy and healthy tissue sparing with high dose-rate FLASH radiotherapy (FLASH-RT) cancer treatment. This technique delivers a prompt high radiation dose rather than fractional doses over time. While some suggest thresholds of > 40 Gy s−1 with a maximal effect at > 100 Gy s−1, accumulated evidence shows that instantaneous dose-rate and irradiation time are critical. Mechanisms are still debated, but toxicity is minimized while inducing apoptosis in malignant tissue. Delivery technologies to date show that a capability gap exists with clinic scale, broad area, deep penetrating, high dose rate systems. Based on these trends, if FLASH-RT is adopted, it may become a dominant approach except in the least technologically advanced countries. The linear induction accelerator (LIA) developed for high instantaneous and high average dose-rate, species independent charged particle acceleration, has yet to be considered for this application. We review the status of LIA technology, explore the physics of bremsstrahlung-converter-target interactions and our work on stabilizing the electron beam. While the gradient of the LIA is low, we present our preliminary work to improve the gradient by an order of magnitude, presenting a point design for a multibeam FLASH-RT system using a single accelerator for application to conformal FLASH-RT.

Dielectric wall accelerators, a class of induction accelerators, employ a novel insulating beam tube to impress a longitudinal electric field on a bunch of charged particles. The surface flashover characteristics of this tube may permit the attainment of accelerating gradients on the order of 100 MV/m for accelerating pulses on the order of a nanosecond in duration. A virtual traveling wave of excitation along the tube is produced at any desired speed by controlling the timing of pulse-generating modules that supply a tangential electric field to the tube wall. Because of the ability to control the speed of this virtual wave, the accelerator is capable of handling any charge-to-mass-ratio particle; hence it can be used for electrons, protons and any ion. The accelerator architectures, key technologies and development challenges will be described.

The typical response of the x-ray converter material to the passage of a high-powered relativistic electron beam is vaporization and rapid dispersal. The effect of this dispersal on subsequent pulses for multi-pulse radiography is the collective effects on the propagation of the electron beam through the expanding plasma and the reduced number of electron to photon interactions. Thus, for the dual-axis radiographic hydrodynamic test facility, the converter material must either be replaced or confined long enough to accommodate the entire pulse train. Typically the 1-mm-thick high Z and full density converter material is chosen to give peak dose and minimum radiographic spot. For repeated pulses we propose a modified converter, constructed of either low density, high Z material in the form of foam or of foils spaced over ten times the axial thickness of the standard 1 mm converter. The converter material is confined within a tube to impede outward motion in radius outside the beam interaction region. We re...

Corkscrew beam motion is caused by chromatic aberration and misalignment of a focusing system. To minimize chromatic aberration, we have developed a time-independent steering algorithm that minimizes the observed corkscrew-amplitude averaged over the beam pulse. The steering algorithm can be done quickly and is not sensitive to the alignment, calibration and spacing of the beam position monitors. The steering algorithm can also be used even if the corkscrew motion caused by a given misaligned magnet is fully developed, i.e., the relative phase advance is greater than 2π. In this paper, we will discuss corkscrew motion, the optimal dynamic alignment procedure, its corkscrew reduction factor, and the effects of beam position monitors' spacing.

The Dielectric Wall Accelerator (DWA) offers the potential to produce a high gradient linear accelerator for proton therapy and other applications. The current status of the DWA for proton therapy will be reviewed. Recent progress in SiC photoconductive switch development will be presented. There are serious beam transport challenges in the DWA arising from short pulse excitation of the wall. Solutions to these transport difficulties will be discussed.

A compact accelerator system architecture based on the dielectric wall accelerator (DWA) for medical proton beam therapy has been developed by the Compact Particle Acceleration Corporation (CPAC). The major subsystems are a Radio Frequency Quadrupole (RFQ) injector linac, a pulsed kicker to select the desired proton bunches, and a DWA linear accelerator incorporating a high gradient insulator (HGI) with stacked Blumleins to produce the required acceleration energy. The Blumleins are switched with solid state laser‐driven optical switches integrated into the Blumlein assemblies. Other subsystems include a high power pulsed laser, fiber optic distribution system, electrical charging system, and beam diagnostics. An engineering prototype has been constructed and characterized, and these results will be used within the next three years to develop an extremely compact 150 MeV system capable of modulating energy, beam current, and spot size on a shot‐to‐shot basis. This paper presents the details the engineering prototype, experimental results, and commercialization plans.

The Heavy-Ion Fusion Accelerator Research Program at Lawrence Berkeley Laboratory has proposed building a 10 MeV induction linac systems experiment, ILSE, to investigate accelerator physics and beam manipulations which are needed or desirable for an induction linac driver. This paper describes the experiments proposed for ILSE: transverse beam combining, drift compression, bending of space-charge-dominated beams, final focus, recirculation, and some studies of beam propagation in the environment of the reactor chamber.

Electron induction linacs have been used for over four decades for a variety of applications. As discussed in Chap. 8, these include basic studies in magnetically confined fusion, transport of intense electron beams in various gases, the generation of electromagnetic radiation from free electron lasers, radiation processing of materials and food, and flash X-ray radiography sources.

Linear Induction Accelerators (LIAs) can readily produce intense electron beams. For example, the ATA accelerator produced a 500 GW beam and the LIU-30 a 4 TW beam (see Chap. 2). Since the induction accelerator concept was proposed in the late 1950s [1, 2], there have been many proposed schemes to convert the beam power to other forms. Categories of applications that have been demonstrated for electron LIAs include

The corkscrew mode in linear accelerators, in which a solenoidal beam-transport system is used, is investigated both analytically and numerically. By assuming that both the acceleration gaps and the drift regions between the adjacent magnets are infinitesimal, it is possible to treat the corkscrew mode analytically and to obtain an expression for the corkscrew mode amplitude and the effective emittance growth as a function of the energy variation within the beam pulse and of the tilts of the injector and the solenoid magnets. Reduction of the corkscrew mode amplitude is possible by an energy compensation scheme. This energy compensation scheme is studied numerically for the Experimental Test Accelerator II (ETA-II) configuration. We find that applying the energy compensation scheme at the beginning of the accelerator can reduce the corkscrew mode amplitude by a factor of two.

An investigation is being made into the feasibility of making a compact proton dielectric wall (DWA) accelerator for medical radiation treatment based on the high gradient insulation (HGI) technology. A small plasma device is used for the proton source. Using only electric focusing fields for transporting and focusing the beam on the patient, the compact DWA proton accelerator system can deliver wide and independent variable ranges of beam currents, energies and spot sizes.

Using the dielectric wall accelerator technology, we are developing a compact induction accelerator system primarily intended for pulsed radiography. Unlike the typical induction accelerator cell that is long compared with its accelerating gap width, the proposed dielectric wall induction accelerator cell is short and its accelerating gap width is comparable with the cell length. In this geometry, the RF modes may be coupled from one cell to the next. We will present recent results of RF modeling of the cells and a prediction of the transverse beam instability on a 2-kA, 8-MeV beam.

Using the high-gradient vacuum dielectric wall accelerator technology, the authors are developing a compact induction accelerator system primarily intended for pulsed X-ray radiography. The accelerator would provide a 2-kA beam for a 20-30 ns flat-top. The design goal is to generate a 2-mm diameter X-ray source. There are two physics designs of the system from the injector to the X-ray converter for two different final energies (8 MeV and 20 MeV). The design goal for the 8-MeV system is to generate 10-rad of X-ray, and the design goal for the 20-MeV system is to generate 300-rad of X-ray. Modeling results were presented and the beam physics in the system were discussed. The predicted spot sizes and the on-axis X-ray doses for both energies were also presented

The second axis of the dual axial radiography hydrodynamic test (DARHT-II) facility at LANL is currently in the commissioning phase. The beam parameters for the DARHT-II machine will be nominally 17 MeV, 2 kA and 1.6 mus. This makes the DARHT-II downstream system the first system ever designed to transport a high current, high energy and long pulse beam [2]. We will test these physics issues of the downstream transport system on a scaled DARHT-II accelerator with a 7.8-MeV and 950-A beam at LANL before commissioning the machine at its full energy and current. The scaling laws for various physics concerns and the beam parameters selection are discussed in this paper.

The DARHT II accelerator at LANL is preparing a series of preliminary tests at the reduced voltage of 7.8 Me V. The transport hardware between the end of the accelerator and the final target magnet was shipped to LLNL and installed on ETA II. Using the ETA II beam at 5.2 MeV we completed a set of experiments designed reduce start up time on the DARHT II experiments and run the equipment in a configuration adapted to the reduced energy. Results of the beam transport using a reduced energy beam, including the kicker and kicker pulser system will be presented.

To produce four short X-ray pulses for radiography, the second-axis of the Dual Axis Radiographic Hydrodynamic Test facility (DARHT-II) will use a fast kicker to select current pulses out of the 2-/spl mu/s duration beam provided by the accelerator. Beam motion during the kicker voltage switching could lead to dilution of the time integrated beam spot and make the spot elliptical. A large elliptical X-ray source produced by those beams would degrade the resolution and make radiographic analysis difficult. We have developed a tuning strategy to eliminate the spot size dilution, and tested the strategy successfully on ETA-II with the DARHT-II kicker hardware.

DARHT-II, the second axis of the Dual-Axis Radiographic Hydrodynamics Test Facility, is being commissioned. DARHT-II is a linear induction accelerator producing 2-microsecond electron beam pulses at 20 MeV and 2 kA. These 2-microsecond pulses will be chopped into four short pulses to produce time resolved X-ray images. Radiographic application requires the DARHT-II beam to have excellent beam quality, and it is important to study various beam effects that may cause quality degradation of a DARHT-II beam. One of the beam dynamic effects under study is "corkscrew" motion. For corkscrew motion, the beam centroid is deflected off axis due to misalignments of the solenoid magnets. The deflection depends on the beam energy variation, which is expected to vary by plusmn0.5% during the "flat-top" part of a beam pulse. Such chromatic aberration will result in broadening of beam spot size. In this paper, we will report simulation results of our study of corkscrew motion in DARHT-II. Sensitivities of beam spot size to various accelerator parameters and the strategy for minimizing corkscrew motion will be described. Measured magnet misalignment is used in the simulation

Summary form only given, as follows. In order to have confidence in the radiation converter target design for DARHT-II using LASNEX and our equation of state (EOS) for Ta, we need to compare the LASNEX simulations with experimental results from ETA-II and laser target experiments. ETA-II experiments include the following measurements: integrated line density, plasma expansion velocity, temperature requirement for hole formation, thermal images of the plasma plume, and foil heating. We will show that agreement between LASNEX simulations and experiments on ETA-II and laser-target experiments is good for essentially all the measurements obtained so far for solid Ta targets. This provides us confidence in the design of the DARHT-II radiation converter target using LASNEX and our eos for Ta. We will also report the comparison of simulations of the latest ETA-II foamed target experiments.

These kickers will be used to make fast dipoles and quadrupoles which are driven by sharp risetime pulsers to provide precision beam manipulation for high current kA electron beams. This technology will be used on the 2/sup nd/ axis of the DARHT linac at LANL. It will be used to provide 4 micropulses of pulse width up to 120 nsec. Selected from a 2 /spl mu/sec., 2 kA, 20 MeV macropulse. The fast pulsers will have amplitude modulation capability to compensate for beam-induced steering effects and other slow beam centroid motion to within the bandwidth of the kicker system. Scaling laws derived from theory will be presented along with extensive experimental data obtained on the test bed ETA-II.

As part of the effort to develop a multi-axis electron beam transport system using stripline kicker technology for DARHT II applications, it is necessary to precisely determine the position and extent of long high energy beams (6-40 MeV, 1-4 kA, 2 microseconds) for accurate position control. The kicker positioning system utilizes shot-to-shot adjustments for reduction of relatively slow (

Improvements have been made in the performance of the ETA-II accelerator that allow a nominal 2 kA, 6 MeV beam to be focused to a spot size less that 1 mm in diameter. The improvements include reducing the energy sweep to less than /spl plusmn/0.5% over 40 ns of the pulse using a real time energy diagnostic and improving the magnetic tune of the accelerator to reduce the emittance to 8 cm-mrad. Finally, an automated tuning system (MAESTRO) was run to minimize the time dependent centroid motion (corkscrew) by adjusting the steering dipoles over the focusing solenoids. The corkscrew motion was reduced to less than /spl plusmn/0.5 mm at the output of the accelerator.

We have used the 2-D PIC code, GYMNOS, to study the transient behaviors in the Heavy Ion Fusion (HIF) injectors. GYMNOS simulations accurately provide the steady state Child-Langmuir current and the beam transient behavior within a planar diode. The simulations of the LBL HIF ESAC injector experiments agree well with the experimental data and EGUN steady state results. Simulations of the nominal EHF injectors have revealed the need to design the accelerating electrodes carefully to control the ion beam current, particularly the ion loss at the end of the bunch as the extraction voltage is reduced. >

It has been shown that the net space-charge forces for a DC beam with space-charge potential depression in a bend have the usual inverse energy square dependence to the first order in the beam radius a over the bend radius R. We extend the analysis to the second order in a/R and allow the beam to have a small transverse displacement. The net space-charge forces are no longer cancelled to inverse energy square factor. The non-cancelled part of self-induced magnetic forces are at the second order in a/R and independent of the beam energy. The nonlinear parts of these forces are much larger than that of the usual inverse energy square forces. Scaling laws for emittance growth caused by the curvature of the beam and a transverse beam displacement, respectively, are presented.

The second axis accelerator of the Dual Axis Radiographic Hydrodynamic Test (DARHT-II) facility will produce a 2-kA, 20-MeV, 2-/spl mu/s output electron beam with a design goal of less than 1000 /spl pi/ mm-mrad normalized transverse emittance. In order to meet this goal, both the beam breakup instability (BBU) and transverse "corkscrew" motion (due to chromatic phase advance) must be limited in growth. Using data from recent experimental measurements of the transverse impedance of actual DARHT-II accelerator cells by Briggs et al., we have used the LLNL BREAKUP code to predict BBU and corkscrew growth in DARHT-II. The results suggest that BBU growth should not seriously degrade the final achievable spot size at the x-ray converter, presuming the initial excitation level is of the order 100 microns or smaller. For control of corkscrew growth, a major concern is the number of "tuning" shots needed to utilize effectively the "tuning-V" algorithm. Presuming that the solenoid magnet alignment falls within spec, we believe that possibly as few as 50-100 shots will be necessary to set the dipole corrector magnet currents. We give some specific examples of tune determination for a hypothetical set of alignment errors.

This paper presents physics design of the DARHT-II downstream system, which consists of a diagnostic beam stop, a novel, fast, high-precision kicker system and the x-ray converter target assembly. The beamline configuration and its beam parameter acceptance, the transverse resistive wall instability modeling, the ion hose instability in the presence of the background gas, and the simulations of beam spill are discussed. We also present the target converter assembly's configuration, and the simulated x-ray spot sizes and doses based on the radiation hydrodynamics code LASNEX and the Monte Carlo radiation transport code MCNP.

The DARHT-II final focusing system consists of a solenoid and a foil, which is used to confine backstreaming ions. The separation between the converter target and the foil needs to be small to minimize the ion focusing effects. The beam spot size on the foil has to be large enough to ensure survivability of the foil while it is being struck by four high current pulses over 2 microsecond period. We have investigated several final focusing lens and focusing schemes. The simulation results of the beam spot size on the target are presented.

The Dual-Axis Radiographic Hydrodynamics Test (DARHT) facility will employ two perpendicular electron Linear Induction Accelerators to produce intense, bremsstrahlung x-ray pulses for flash radiography. We intend to produce measurements containing three-dimensional information with sub-millimeter spatial resolution of the interior features of very dense, explosively-driven objects. The facility will be completed in two phases with the first phase having become operational in July 1999 utilizing a single-pulse, 20-MeV, 2-kA, 60-ns accelerator, a high-resolution electro-optical x-ray imaging system, and other hydrodynamics testing systems. We will briefly describe this machine. The first electron beams will be generated in the second phase of DARHT this year. The second DARHT accelerator consists of a 18.4-MeV, 2-kA, 2-microsecond pulse-width accelerator. Four short electron micropulses of variable pulse-width and spacing will be chopped out of the original, long accelerator pulse for producing time-resolved x-ray images. The second phase also features an extended, high-resolution electro-optical x-ray system with a framing speed of about 2-MHz. We will discuss this accelerator by summarizing the overall design of the long-pulse injector and accelerator. We will also discuss the fast kicker used to separate the long-pulse beam into short bursts suitable for radiography.

Ions extracted from a solid surface or plasma by impact of an high intensity and high current electron beam can partially neutralize the beam space charge and change the focusing system. We have investigated ion emission computationally and experimentally. By matching PIC simulation results with available experimental data, our finding suggests that if a mix of ion species is available at the emitting surface, protons dominate the backstreaming ion effects, and that, unless there is surface flashover, ion emission is source limited. We have also investigated mitigation, such as e‐beam cleaning, laser cleaning and ion trapping with a foil barrier. The temporal behavior of beam spot size with a foil barrier and a focusing scheme to improve foil barrier performance are discussed.

During normal DARHT II operation, the beam exiting the accelerator will be well characterized by its nominal design parameters of 20-MeV, 2000-Amperes, 2-/spl mu/sec-pulse length, and 3 cm-mr unnormalized emittance. Normal operation will have the beam delivered to a beam dump via several DC magnets. A 2-way kicker magnet is used to deflect portions of the beam into the straight ahead beamline leading to either a diagnostic beamline or to the converter target beamline. During start up and or beam development periods, the beam exiting the accelerator may have parameters outside the acceptable range of values for normal operation. The Enge beamline must accommodate this range of unacceptable beam parameters, delivering the entire 80 KiloJoule of beam to the dump even though the energy, emittance, and/or match is outside the nominal design range.

The accelerator on the second-axis of the Dual-Axis Radiographic Hydrodynamic Test (DARHT-II) Facility will generate a 20 MeV, 2-4 kA, 2 /spl mu/s long electron beam with an energy variation /spl les//spl plusmn/0.5%. Four short current pulses with various lengths will be selected out of this 2 /spl mu/s long current pulse and delivered to an X-ray converter target. The DARHT-II radiographic resolution requires these electron pulses to be focused to sub-millimeter spots on bremsstrahlung targets with peak-to-peak transverse beam motion less than a few hundred microns. We have modeled the transverse beam motion, including the beam breakup instability, corkscrew motion, transverse resistive wall instability and beam induced transverse deflection in the kicker system, from the DARHT-II injector exit to the X-ray converter target. Simulations show that the transverse motion at the X-ray converters satisfies the DARHT-II radiographic requirements.

Four short current pulses with various pulse widths and spacing will be delivered to the X-ray converter target on the second-axis of the Dual-Axis Radiographic Hydrodynamic Test (DARHT-II) facility. To ensure that the DARHT-II multi-pulse target will provide enough target material for X-ray production for all four pulses, the target needs either to survive the strike of four electron pulses or to accommodate target replenishment. A distributed target may survive hitting of four electron pulses. For target replenishment, two types of target configurations are being considered: stationary target systems with beam repositioning and dynamic moving target systems. We compare these three target systems and their radiographic performance.

The accelerator for the second axis of the Dual Axis Radiographic Hydrodynamic Test (DARHT) facility will produce a 4-kA, 20-MeV, 2-/spl mu/s output electron beam with a design goal of less than 1000 /spl pi/ mm-mrad normalized transverse emittance and less than 0.5-mm beam centroid motion. In order to meet this goal, the beam transport must have excellent optics and the beam breakup instability (BBU) must be limited in growth. Using a number of simulation codes such as AMOS and BREAKUP, we have modeled the transverse impedances of the DARHT-II accelerator cells and the electron beam response to different transverse excitations such as injector RF noise, magnetic dipole fields arising from the 90-degree bend between the cathode stalk and insulator column, and downstream solenoid alignment errors. The very low Q (/spl sim/2) predicted for the most important TM dipole modes has prompted us to extend the BREAKUP code to be able to use the dipole wakefields calculated by AMOS in addition to the most usual discrete frequency BBU mode model. We present results for the predicted BBU growth and the empirical sensitivity to various machine parameters.

A new algorithm for space charge emission has been developed to provide the correct (to a few percent) Child‐Langmuir steady‐state current limits as the number of mesh points in the voltage gap drops to O(10). Further, the transient behavior of such flows compares well with idealized, analytic cases, lending confidence as we extend these algorithms into full RZ geometry with curved emitting surfaces to investigate transient characteristics of realistic injector designs.

An ideal rf photocathode gun in a π-mode configuration supporting only a single mode with no nonlinear rf field is studied numerically by using the simulation code PARMELA. For a given electron bunch, the normalized emittance can be minimized. Both the minimum normalized emittance and the optimized accelerating field are proportional to the square root of the peak current. Three possible rf photocathode guns for LLNL-SLAC-LBL 1 GeV test are simulated. It is found that both a 2 ps half-width bunch and a 6 ps half-width bunch with the transverse emittance roughly 8–17 mmm mrad and 1 nC charge per bunch can be generated by guns with (1) ƒ = 1269 MHz , E 0 = 30 MV/m; (2) ƒ = 1269 MHz , E 0 = 60 MV/m; and (3) ƒ = 2856 MHz , E 0 = 60 MV/m. Here, ƒ is the rf frequency, and E 0 is the peak accelerating field.

The driving current of a free electron laser is calculated by including terms, generally neglected, which represent the effect of the e-beam bending due to the electron wiggling. The 3D wave equation is solved by representing the field as a superposition of space harmonics. The transverse distribution of the field is accounted for by expanding it in a series of Gauss-Laguerre modes. A simple expression of the correction on the complex propagation constant caused by the electron wiggling is obtained.

The driving current of a free-electron laser is calculated by solving a linearized Boltzmann equation for a relativistic electron beam. Particular attention is paid to terms, generally neglected, which represent the effect of the electron-beam bending due to the finite radius of the electron wiggling. In solving the three-dimensional Helmholtz equation for a laser driven by a source varying periodically with the period of the wiggler, the laser field is represented as a superposition of space harmonics whose longitudinal propagation constants differ by multiples of the wiggler period (Bloch waves). In addition, the transverse distribution of the field is analyzed by expanding it as a series of Gauss?Laguerre modes.

The effect on optical guiding of the undulations of an electron beam in an FEL is investigated, and a model for a fully saturated FEL amplifier with no remaining gain is developed. The density of the electrom beam in the model fully includes the effects of both transverse and longitudinal undulation of the beam. The longitudinal density modulation is expressed in terms of the Bessel functions of ζ, where ζ = a w 2 2(1 + a w 2 ) is the shift of the electron phase in the electron bucket caused by its longitudinal undulation. The transverse density modulation is evaluated to second order in the ratio of undulation amplitude δr to beam radial scale length rb. The radiation field from the modeled beam is calculated in terms of spatial modes proportional to exp[i(k + δk + lkw)z − iωt], where l is an arbitrary integer. Here, δk is the change of the wavenumber of the radiation caused by the electron bunches. Radially radiating modes with intensity on the order of ( δk k w )ζ 2 are found. Optical guiding is found to be modified by the transverse undulations of the beam at second order in δr r b , and by the longitudinal undulations to first order in δk k w . For the usual FEL parameters, the correction is quite small.

The driving current of a free-electron laser with a uniform helical undulator is calculated by solving a linearized Boltzmann equation which includes terms, generally neglected, representing the effect of the {ital e}-beam bending due to the finite radius of the electron wiggling. The current is used for writing the wave equation for the electromagnetic field amplified along the {ital z} axis of the wiggler. The space modulation of the current induced by the {ital e}-beam bending is eliminated by using a moving frame obtained by displacing the coordinate system, with its origin at the center of the wiggler entrance section, along the central trajectory of the electron beam. In this way, a parabolic wave equation is obtained similar to the well-known equation of high-gain lasers, with the addition of a term proportional to the wiggling radius and the transverse gradient of the field, which depends sinusoidally on {ital z}. For solving this generalized parabolic equation, the laser field is represented in the moving frame as a superposition of space harmonics whose longitudinal propagation constants differ by multiples of the wiggler period (Bloch-Floquet waves). The transverse profile of the field is accounted for by expanding it in a series of Gauss-Laguerremore » wave functions. Then, combining Bloch-Floquet waves with Gauss-Laguerre wave functions, three-dimensional mutually orthogonal modes are obtained. In the laboratory frame these modes appear as wiggling beams, which are used as the basis for transforming the wave equation into a homogeneous set of linear equations. A simple expression for the correction of the propagation constant due to the {ital e}-beam bending is presented together with the analytic expression of the field for the case of high Fresnel numbers.« less

The linear properties and saturation mechanisms of the lower‐hybrid drift instability have been investigated using a one‐dimensional particle‐hybrid simulation. For low drift velocities (vd≪vti), ion trapping and current relaxation (vd→0) are competing processes for stabilization. If the relative electron–ion drift velocity is kept constant in time, ion trapping causes the end of instability growth; if this drift is allowed to decrease consistent with momentum balance, then saturation is due to current relaxation.

It is found that a finite perturbations of the ion orbits leads to a nonlinear frequency shift that reduces the mode frequency and has a weak stabilizing effect on the lower‐hybrid drift instability. This result is obtained from a self‐consistent solution of the Vlasov–Poisson equations using perturbation theory in which the nonlinear dielectric function and the nonlinear temporal evolution of a single unstable mode in the low drift velocity regime are calculated analytically. The nonlinear frequency shift does not seem to be a potent saturation mechanism in a collisionless plasma, but may be more relevant when there are ion‐ion collisions.