Space-charge limiting currents for magnetically focused intense relativistic electron beams

The self-consistent differential equations, which describe a laminar-flow equilibrium state in a magnetically focused intense relativistic electron beam propagating inside a conducting waveguide, are presented. The canonical angular momentum, Pe, defined under the conditions at the source, uniquely determines the possible solutions of these equations. By numerically solving these equations, the space-charge limited current and the externally applied magnetic field are obtained in a solid beam and a hollow beam in two cases of Pθ= 0 （magnetically shielded source） and Pθ= const. （immersed source） separately. It is shown that the hollow beam is more beneficial to the propagation of the intense relativistic beam through a drift tube than the solid beam.

Effects of anode material on the evolution of anode plasma and characteristics of intense electron beam diode

In this paper,three kinds of materials including graphite,titanium(Ti)and molybdenum(Mo)are used as anodes to figure out the influence factors of anode material on the characteristics of the intense electron beam diode.The results show that the characteristics of diode are mainly determined by the cathode plasma motion under a 15 mm diode gap,in which the typical electron beam parameters are 280 kV,3.5 kA.When the diode gap is reduced to 5 mm,the voltage of the electron beam reduces to about 200 kV,and its current increases to more than 8.2 kA.It is calculated that the surface temperatures of Ti and Mo anodes are higher than their melting points.The diode plasma luminescence images show that Ti and Mo anodes produce plasmas soon after the bombardment of electron beams.Ti and Mo lines are respectively found in the plasma composition of Ti and Mo anode diodes.Surface melting traces are also observed on Ti and Mo anodes by comparing the micromorphologies before and after bombardment of the electron beam.These results suggest that the time of anode plasma generation is closely related to the anode material.Compared with graphite,metal Ti and Mo anodes are more likely to produce large amounts of plasma due to their more significant temperature rise effect.According to the moment that anode plasma begins to generate,the average expansion velocities of cathode and anode plasma are estimated by fitting the improved space-charge limited flow model.This reveals that generation and motion of the anode plasma significantly affect the characteristics of intense electron beam diode.

Consistency of the directionality of partially coherent beams in turbulence expressed in terms of the angular spread and the far-field average intensity

Under the quadratic approximation of the Rytov＇s phase structure function, this paper derives the general closed-form expressions for the mean-squared width and the angular spread of partially coherent beams in turbulence. It finds that under a certain condition different types of partially coherent beams may have the same directionality as a fully coherent Gaussian beam in free space and also in atmospheric turbulence if the angular spread is chosen as the characteristic parameter of beam directionality. On the other hand, it shows that generally, the directionality of partially coherent beams expressed in terms of the angular spread is not consistent with that in terms of the normalized far-field average intensity distribution in free space, but the consistency can be achieved due to turbulence.

Effect of longitudinal applied magnetic field on the self-pinched critical current in intense electron beam diode

The effect of applied longitudinal magnetic field on the self-pinched critical current in the intense electron beam diode is discussed. The self-pinched critical current is derived and its validity is tested by numerical simulations. The results shows that an applied longitudinal magnetic field tends to increase the self-pinched critical current. Without the effect of anode plasma, the maximal diode current approximately equals the self-pinched critical current with the longitudinal magnetic field applied; when self-pinched occurs, the diode current approaches the self-pinched critical current.

Hydrodynamic Effects on Surface Morphology Evolution of Titanium Alloy under Intense Pulsed Ion Beam Irradiation

The hydrodynamic effects of molten surface of titanium alloy on the morphology evolution by intense pulsed ion beam （IPIB） irradiation are studied. It is experimentally revealed that under irradiation of IPIB pulses, the surface morphology of titanium alloy in a spatial scale of μm exhibits an obvious smoothening trend. The mechanism of this phenomenon is explained by the mass transfer caused by the surface tension of molten metal. Hydrodynamic simulation with a combination of the finite element method and the level set method reveals that the change in curvature on the molten surface leads to uneven distribution of surface tension. Mass transfer is caused by the relief of surface tension, and meanwhile a flattening trend in the surface morphology evolution is achieved.

Calculation of Beam Intensity Distribution for the Neutral Beam Injection in EAST

Theoretical beam intensity distribution is derived for the neutral-beam-injection ion source with a multi-slot extraction in EAST. The beam intensity profile, both along and perpendicular to the injecting direction and the beam power deposition to the inner elements in the neutral beam injector （NBI） are evaluated. The results indicate that the transverse beam intensity is much higher than the longitudinal one. This study could provide information for the design of vacuum system, structure of inner elements and cooling system of the neutral beam injector in EAST.

Warm dense matter research at HIAF

The research activities on warm dense matter driven by intense heavy ion beams at the new project High Intensity heavy-ion AcceleratorFacility (HIAF) are presented. The ion beam parameters and the simulated accessible state of matter at HIAF are introduced, respectively. Theprogresses of the developed diagnostics for warm dense matter research including high energy electron radiography, multiple-channel pyrometer,in-situ energy loss and charge state of ion detector are briefly introduced.

Using a pre-kicker to ensure safe extractions from the HEPS storage ring

The High Energy Photon Source(HEPS)is a 6 GeV diffraction-limited storage ring light source under construction.The swap-out injection is adopted with the depleted bunch recycled via high-energy accumulation in the booster.The extremely high beam energy density of the bunches with an ultra-low emittance(about 30 pm horizontally and 3 pm vertically)and high bunch charges(from 1.33 to 14.4 nC)extracted from the storage ring could cause hazardous damage to the extraction Lambertson magnet in case of extraction kicker failure.To this end,we proposed the use of a pre-kicker to spoil the bunches prior to extraction,significantly reducing the maximum beam energy density down to within a safe region while still maintaining highly efficient extractions.The main parameters of the pre-kicker are simulated and discussed.

Relation between space-charge-limiting current and electric field enhancement factor at curved surface cathode

A two-dimensional solution of space-charge-limiting current for a high current vacuum diode with a spherical cathode is presented. The relation between space-charge-limiting current and electric field enhancement factor at the cathode surface for the diode with a curved surface cathode is also discussed. It is shown that compared with the current given by the conventional Child-Langmuir law, which describes the one-dimensional space-charege-limiting current, the two-dimensional space-charge-limiting current in such a diode is enhanced due to the electric-field enhancement along the cathode surface. Among practical parameter ranges, enhancement factor ηb approximately satisfies ηb Aβn, where β is the electric field enhancement factor at the cathode surface, and n is a constant between 1 and 2, which is confirmed to be universal for the diodes with curved surface cathodes.

Two-dimensional numerical research on effects of titanium target bombarded by TEMPⅡ accelerator

Two-dimensional numerical research has been carried out on the ablation effects of titanium target irradiated by intense pulsed ion beam （IPIB） generated by TEMP Ⅱ accelerator. Temporal and spatial evolution of the ablation process of the target during a pulse time has been simulated. We have come to the conclusion that the melting and evaporating process begin from the surface and the target is ablated layer by layer when the target is irradiated by the IPIB. Meanwhile, we also obtained the result that the average ablation velocity in target central region is about 10 m/s, which is far less than the ejection velocity of the plume plasma formed by irradiation. Different effects have been compared to the different ratio of the ions and different energy density of IPIB while the target is irradiated by pulsed beams.

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.

Theoretical investigation of an electron beam propagating through a wide gap cavity

This paper presents a self-consistent nonlinear theory of the current and energy modulations when an electron beam propagates through an inductively-loaded wide gap cavity. The integro-differential equations axe obtained to describe the modulation of the beam current and kinetic energy. A relativistic klystron amplifier （RKA） model is introduced, which uses an inductively-loaded wide gap cavity as an input cavity. And a numerical code is developed for the extended model based on the equations, from which some relations about the modulated current and modulated energy are numerically given.

Numerical Research on Plasma Generation and Expansion into Vacuum

Energy deposition of intense pulsed ion beam （IPIB） on the Ti target based on the 2D model of IPIB density has been simulated by the Monte Carlo （MC） method. Taking the deposited energy as the thermal source, we have established the ablation model of the target and calculated the spatial and temporal evolution of the ablation shape of the Ti target irradiated by IPIB with different energy densities. We have also established the ejection model of the hydrodynamic equations related to the ablation shape of the target by using the ablation results as the initial conditions of plasma formed by IPIB irradiation. The spatially and temporally evoluted profiles of the plasma pressure and mass density are calculated.

The Propagation Characteristics of the Electron Beam with Initial Modulation

The propagation characteristics of the beam under various initial conditions are in-vestigated by means of PIC method.The influences of density modulation and velocity modulationon the propagation characteristics are discussed and compared.The results reveal that by chang-iug the amplitude of the two kinds of modulations and the phase difference between them,the

Design and development of the beamline for a proton therapy system

A proton therapy(PT)facility with multiple treatment rooms based on the superconducting cyclotron scheme is under development at Huazhong University of Science and Technology(HUST).This paper attempts to describe the design considerations and implementation of the PT beamline from a systematic viewpoint.Design considerations covering beam optics and the influence of high-order aberrations,beam energy/intensity modulation,and beam orbit correction are described.In addition to the technical implementation of the main beamline components and subsystems,including the energy degrader,fast kicker,beamline magnets,beam diagnostic system,and beamline control system are introduced.

Forward acceleration and generation of femtosecond megaelectronvolt electron beams by an ultrafast intense laser pulse

We present a new mechanism of energy gain of electrons accelerated by a laser pulse. It is shown that when the intensity of an Tiltrafast intense laser pulse decreases rapidly along the direction of propagation, electrons leaving the pulse experience an action of ponderomotive deceleration at the descending part of a lower-intensity laser field than acceleration at the ascending part of a high-intensity field, thus gain net energy from the pulse and move directly forward. By means of such a mechanism, a megaelectronvolt electron beam with a bunch length shorter than 100 fs could be realized with an ultrafast (≤30 fs), intense (≥1019 W/cm2) laser pulse.

A fast emittance measurement unit for high intensity DC beam

A combined unit, which has the ability to measure the current and emittance of the high intensity direct current（DC）ion beam, is developed at Peking University（PKU）. It is a multi-slit single-wire（MSSW）-type beam emittance meter combined with a water-cooled Faraday Cup, named high intensity beam emittance measurement unit-6（HIBEMU-6）. It takes about 15 seconds to complete one measurement of the beam current and its emittance. The emittance of a 50-mA@50-kV DC proton beam is measured.

Computer simulations for intense continuous beam transport in electrostatic lens systems

A code LEADS based on the Lie algebraic analysis for the continuous beam dynamics with space charge effect in beam transport has been developed. The program is used for the simulations of axial-symmetric and unsymmetrical intense continuous beam in the channels including drift spaces, electrostatic lenses and DC electrostatic accelerating tubes. In order to get the accuracy required, all elements are divided into many small segments, and the electric field in the segments is regarded as uniform field, and the dividing points are treated as thin lenses. Iteration procedures are adopted in the program to obtain self-consistent solutions. The code can be used in the designs of low energy beam transport systems, electrostatic accelerators and ion implantation machines.

Intense DC beam nonlinear transport-analysis & simulation

The intense dc beam nonlinear transport was analyzed with the Lie algebraic method, and the particle trajectories of the second order approximation were obtained. Based on the theoretical analysis a computer code was designed. To get self-consistent solutions, iteration procedures were used in the code. As an example, we calculated a beam line (drift-electrostatic quadrupole doublet-drift). The results agree to the results calculated by using the PIC method.

Comparison of the PIC model and the Lie algebraic method in the simulation of intense continuous beam transport

Both the PIC (Particle-In-Cell) model and the Lie algebraic method can be used to simulate the transport of intense continuous beams. The PIC model is to calculate the space charge field, which is blended into the external field, and then simulate the trajectories of particles in the total field; the Lie algebraic method is to simulate the intense continuous beam transport with transport matrixes. Two simulation codes based on the two methods are developed respectively, and the simulated results of transport in a set of electrostatic lenses are compared. It is found that the results from the two codes are in agreement with each other, and both approaches have their own merits.