A. Goswami

Envelope equations for cylindrically symmetric space charge dominated multi species beam

We have derived differential equations for the beam envelope of a cylindrically symmetric space charge dominated multi-species beam. The major contribution here is the inclusion of the emittance growth of each species of the beam resulting from the nonlinear space charge effect of the other species which arises if the beam radius of that particular species is greater than the other species. In addition, we have also discussed the beam selection using slits and considered only the effective values of the current and emittance of each species after the slit for further transport in case the beam size of any species is larger than the slit size or the finite aperture of the beam pipe. Finally, we have studied the transport of proton from 2.45 GHz microwave ion source in the presence of H2+, H3+ species to demonstrate the application of these results. Numerical results are presented for various values of the total beam current and different fractions of p, H2+, and H3+ species.

A Vlasov equilibrium for space charge dominated beam in a misaligned solenoidal channel

The effect of displacement and rotational misalignments of solenoid magnets with respect to the ideal beam propagation axis on the dynamics of intense charged particle beams have been studied. The equation of motion of the beam centroid has been obtained and found to be independent of any specific beam distribution. A Vlasov equilibrium distribution for the intense beam propagation through misaligned focussing channel has been obtained. Self-consistent simulation confirms the analytical result.

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.

Studies on space charge neutralization and emittance measurement of beam from microwave ion source

A 2.45 GHz microwave ion source together with a beam transport system has been developed at VECC to study the problems related with the injection of high current beam into a compact cyclotron. This paper presents the results of beam profile measurement of high current proton beam at different degrees of space charge neutralisation with the introduction of neon gas in the beam line using a fine leak valve. The beam profiles have been measured at different pressures in the beam line by capturing the residual gas fluorescence using a CCD camera. It has been found that with space charge compensation at the present current level (∼5 mA at 75 keV), it is possible to reduce the beam spot size by ∼34%. We have measured the variation of beam profile as a function of the current in the solenoid magnet under the neutralised condition and used these data to estimate the rms emittance of the beam. Simulations performed using equivalent Kapchinsky-Vladimirsky beam envelope equations with space charge neutralization factor are also presented to interpret the experimental results.

Effect of image charge on the off-axis transport of intense beams in a small aperture quadrupole lattice

This paper investigates the first order image charge effects of circular conducting pipe on an intense off-axis continuous charged particle beam propagating through an alternating-gradient focusing channel. The equations of motion for the centroid and envelopes of slightly off-axis beam are derived and used to determine the equilibrium and stability conditions for the beam transport. The envelope oscillation frequencies of the mismatched beam are obtained by the smooth approximation method and by numerical evaluation of the linearly perturbed envelope equations. Depending on the beam intensity and focusing parameters, it is found that the frequency of the out-of-phase mode of envelope oscillation is reduced due to the presence of the conducting wall. Detailed numerical results for off-axis beam transport in a quadrupole lattice are presented and the stable regimes in the parameter space are determined numerically. It is observed that the unstable region for the envelope evolution with image charge effects...

Kinetic equilibrium of space charge dominated beams in a misaligned quadrupole focusing channel

The dynamics of intense beam propagation through the misaligned quadrupole focusing channel has been studied in a self-consistent manner using nonlinear Vlasov-Maxwell equations. The equations of motion of the beam centroid have been developed and found to be independent of any specific beam distribution. A Vlasov equilibrium distribution and beam envelope equations have been obtained, which provide us a theoretical tool to investigate the dynamics of intense beam propagating in a misaligned quadrupole focusing channel. It is shown that the displaced quadrupoles only cause the centroid of the beam to wander off axis. The beam envelope around the centroid obeys the familiar Kapchinskij-Vladimirskij envelope equation that is independent of the centroid motion. However, the rotation of the quadrupole about its optical axis affects the beam envelope and causes an increase in the projected emittances in the two transverse planes due to the inter-plane coupling.

Transport characteristics of a Glaser magnet for an axisymmetric and non-axisymmetric space charge dominated beam

This paper describes the dynamics of space charge dominated beam through a Glaser magnet which is often used to focus charged particle beams in the low energy section of accelerators and in many other devices. Various beam optical properties of the magnet and emittance evolution that results from the coupling between the two transverse planes are studied. We have derived ten independent first order differential equations for the beam sigma matrix elements assuming the linear space-charge force consistent with the assumption of the canonically transformed KV like distribution. In addition, the feasibility of using a Glaser magnet doublet in a low energy beam injection line to match an initial non-axisymmetric high intensity beam with net angular momentum to an axisymmetric system to suppress effective emittance growth after transition back to an uncoupled system, has also been studied.

Effect of nonuniform radial density distribution on the space charge dominated beam bunching

Beam dynamics of a space charge dominated beam during the bunch compression is studied self consistently for the case of fixed shape non-uniform bell shape and hollow shape density distributions in the transverse direction. We have used thick slices at different parts of the beam to account for variation in the beam radius in the study of the transverse dynamics. The longitudinal dynamics has been studied using the disc model. The axial variation of the radius of the slices and emittance growth arising from the phase dependence of the transverse rf forces are also included in the simulation. We have modified the beam envelope equation to take into account the longitudinal space charge effect on the transverse motion which arises due to the finite bunch size. To demonstrate the application of the theoretical formulations developed, we have studied a sinusoidal beam bunching system and presented detailed numerical results.

Transport of intense proton beam in the presence of subdominant species in a low energy beam transport system

The dynamics of space-charge-dominated low energy proton beam in the presence of H2+ and H3+ beams has been studied in a solenoid based transport system using particle-in-cell (PIC) simulation method. Multispecies envelope equation and random search technique have been used to transport and match the primary beam considering two options. The PIC simulation shows the formation of hollow distribution of H2+ and H3+ beams around the proton beam in the first case where the waist of the proton beam is formed in between the solenoids and it is absent in the second case where the beam size is kept large in between the solenoids. Separation of hollow distribution appears more distinct as the proton fraction is increased and is almost independent of the combination of H2+ and H3+ beams for a given proton fraction. This effect helps to reject the unwanted species more effectively. The evolution of rms size and emittance of the proton beam has been studied in the presence of a circular aperture using KV and Gaussian distributions for the species in both the cases.

Effect of subdominant species on the evolution of intense primary beam in a low energy beam transport line

The dynamics of space-charge-dominated multispecies beam with different distributions has been studied in a solenoid based low energy beam transport line using a particle-in-cell simulation method. Results are presented in wide parameter regimes covering emittance dominated as well as space charge dominated multispecies beams consisting of p, H2+, and H3+ beams. Simulation shows the formation of hollow distribution of H2+ and H3+ beams around the desired proton beam and separation is more distinct as the fraction of proton is increased. The hollow formation is almost independent of combination of H2+ and H3+ beams, once the fraction of proton beam is fixed. The emittance growth of proton is found to increase sharply in the space-charge-dominated regime and is more in the cases where proton fraction is low.