Search Results (34 total)

Simulations of charged particle beams in accelerator cavities show that a two-dimensional photonic crystal can be used to create a three-dimensional hybrid cavity with a single operating mode and no significant higher order modes, greatly reducing long-range wakefields. Optimizing the photonic crystal cavity to reduce radiation leakage in the desired mode (of a finite-sized structure) yields even lower wakefields. Wakefields in photonic crystal cavities are compared to those in metal pillbox cavities.

Guiding-center theory provides the reduced dynamical equations for the motion of charged particles in slowly varying electromagnetic fields, when the fields have weak variations over a gyration radius (or gyroradius) in space and a gyration period (or gyroperiod) in time. Canonical and noncanonical Hamiltonian formulations of guiding-center motion offer improvements over non-Hamiltonian formulations: Hamiltonian formulations possess Noether’s theorem (hence invariants follow from symmetries), and they preserve the Poincaré invariants (so that spurious attractors are prevented from appearing in simulations of guiding-center dynamics). Hamiltonian guiding-center theory is guaranteed to have an energy conservation law for time-independent fields—something that is not true of non-Hamiltonian guiding-center theories. The use of the phase-space Lagrangian approach facilitates this development, as there is no need to transform a priori to canonical coordinates, such as flux coordinates, which have less physical meaning. The theory of Hamiltonian dynamics is reviewed, and is used to derive the noncanonical Hamiltonian theory of guiding-center motion. This theory is further explored within the context of magnetic flux coordinates, including the generic form along with those applicable to systems in which the magnetic fields lie on nested tori. It is shown how to return to canonical coordinates to arbitrary accuracy by the Hazeltine-Meiss method and by a perturbation theory applied to the phase-space Lagrangian. This noncanonical Hamiltonian theory is used to derive the higher-order corrections to the magnetic moment adiabatic invariant and to compute the longitudinal adiabatic invariant. Noncanonical guiding-center theory is also developed for relativistic dynamics, where covariant and noncovariant results are presented. The latter is important for computations in which it is convenient to use the ordinary time as the independent variable rather than the proper time. The final section uses noncanonical guiding-center theory to discuss the dynamics of particles in systems in which the magnetic-field lines lie on nested toroidal flux surfaces. A hierarchy in the extent to which particles move off of flux surfaces is established. This hierarchy extends from no motion off flux surfaces for any particle to no average motion off flux surfaces for particular types of particles. Future work in magnetically confined plasmas may make use of this hierarchy in designing systems that minimize transport losses.

The interaction of a circularly polarized laser pulse with a mixed solid target containing two species of ions is studied by particle in cell simulations and analytical model. After the interaction tends to be stable, it is demonstrated that the acceleration is more efficient for the heavier ions than that in plasmas containing a single kind of heavy ion and the acceleration efficiency is higher when its proportion is lower. To obtain monoenergetic heavy-ion beams, a sandwich target with a thin mixed ion layer between two light ion layers and a microstructured target are proposed. The influences of parameters of the laser pulse and target on ion acceleration are discussed in detail. It is found that, when the target is thick enough, a cold target is more appropriate for heavy-ion acceleration than a warm target, and the velocity of the reflected heavy ions is proportional to the laser amplitude.

A method for efficient laser acceleration of heavy ions by electrostatic shock is investigated using particle-in-cell (PIC) simulation and analytical modeling. When a small number of heavy ions are mixed with light ions, the heavy ions can be accelerated to the same velocity as the light ions so that they gain much higher energy because of their large mass. Accordingly, a sandwich target design with a thin compound ion layer between two light-ion layers and a micro-structured target design are proposed for obtaining monoenergetic heavy-ion beams.

Plasma density gradients in a gas jet were used to control the wake phase velocity and trapping threshold in a laser wakefield accelerator, producing stable electron bunches with longitudinal and transverse momentum spreads more than 10 times lower than in previous experiments (0.17 and 0.02  MeV/c FWHM, respectively) and with central momenta of 0.76±0.02  MeV/c. Transition radiation measurements combined with simulations indicated that the bunches can be used as a wakefield accelerator injector to produce stable beams with 0.2  MeV/c-class momentum spread at high energies.

The origin of beam disparity in emittance and betatron oscillation orbits, in and out of the polarization plane of the drive laser of laser-plasma accelerators, is explained in terms of betatron oscillations driven by the laser field. As trapped electrons accelerate, they move forward and interact with the laser pulse. For the bubble regime, a simple model is presented to describe this interaction in terms of a harmonic oscillator with a driving force from the laser and a restoring force from the plasma wake field. The resulting beam oscillations in the polarization plane, with period approximately the wavelength of the driving laser, increase emittance in that plane and cause microbunching of the beam. These effects are observed directly in 3D particle-in-cell simulations.

In the injection of electron-Bernstein waves (EBW) into a plasma, proposed for plasma heating and current drive in over-dense plasma, conversion of the fundamental to its second harmonic is predicted analytically and observed in computations. The mechanism is traced to the existence of locations where one can have both wave number and frequency matching between the fundamental and its harmonic. Further, at such locations, the second harmonic commonly has minimal group velocity, and this allows the amplitude of the second harmonic to build to values exceeding that of the fundamental at power levels less than anticipated in experiments. The second-harmonic power can then be deposited at half-harmonic resonances of the original wave, often far from the desired location of energy deposition. Estimates for the power at which this is significant are given.

The equation describing the propagation of a mode driven by external currents in an inhomogeneous dielectric is derived from the principle of the conservation of wave energy density and wave momentum density. The wave amplitude in steady state is obtained in terms of a simple spatial integration of the driving current. The contribution from the spatial derivative of the dielectric response is found to be important. The analytical predictions are verified through comparison with δf particle-in-cell computations of electron Bernstein wave propagation, thus showing applicability to kinetic systems.

Fundamental advances in experimental nuclear physics will require ion beams with orders of magnitude luminosity increase and temperature reduction. One of the most promising particle accelerator techniques for achieving these goals is electron cooling, where the ion beam repeatedly transfers thermal energy to a copropagating electron beam. The dynamical friction force on a fully ionized gold ion moving through magnetized and unmagnetized electron distributions has been simulated, using molecular dynamics techniques that resolve close binary collisions. We present a comprehensive examination of theoretical models in use by the electron cooling community. Differences in these models are clarified, enabling the accurate design of future electron cooling systems for relativistic ion accelerators.

This paper demonstrates that transverse beam halos can be controlled by combining nonlinear focusing and collimation. The study relies on one-dimensional, constant focusing particle-in-cell (PIC) simulations and a particle-core model. Beams with linear and nonlinear focusing are studied. Calculations with linear focusing confirm previous findings that the extent and density of the halo depend strongly upon the initial mismatch of the beam. Calculations with nonlinear focusing are used to study damping in the beam oscillations caused by the mismatch. Although the nonlinear force damps the beam oscillations, it is accompanied by emittance growth. This process is very rapid and happens within the first 2–3 envelope oscillations. After this, when the halo is collimated using a system of four collimators, further evolution of the beam shows that the halo is not regenerated. The elimination of the beam halo could allow either a smaller physical aperture for the transport system or it could allow a beam of higher current in a system with the same physical aperture. This advantage compensates for the loss of particles due to collimation.

The optimal values of Q and Δω (Δω≡ω−Ω) for cooling a pure electron plasma with a microwave bath have been calculated. An electron plasma, which has no internal degree of freedom, cannot be cooled below the temperature of a heat bath. However, longitudinal cooling can be achieved by energy transfer from the poorly cooled longitudinal degree of freedom to the well-cooled (by synchrotron radiation) transverse degree of freedom. To do this, a microwave bath is introduced to the electron plasma. A microwave tuned to a frequency below the gyrofrequency forces electrons moving towards the microwave to absorb a microwave photon. The electrons move up one in Landau state and then lose their longitudinal momenta. In this process, the longitudinal temperature of the electron plasma decreases. On the basis that the perpendicular temperature is below the Landau temperature of the plasma, we set up two level transition equations and then derive a Fokker-Planck equation from them. With the aid of a finite element method (FEM) code for the equation, the cooling times for several values of the magnetic field, the microwave cavity (Q), and the relative detuning frequency from the gyrofrequency (Δω) are calculated. Thus optimal values of the microwave cavity and the detuning frequency for longitudinal cooling of a strongly magnetized electron plasma with a microwave bath have been found. By applying these optimal values with an appropriate microwave intensity, the best cooling can be obtained. For an electron plasma magnetized to 10  T, the cooling time to the solid state is approximately two hours.

A condition for improved dynamic aperture for nonlinear, alternating gradient transport systems is derived using Lie transform perturbation theory. The Lie transform perturbation method is used here to perform averaging over fast oscillations by canonically transforming to slowly oscillating variables. This is first demonstrated for a linear sinusoidal focusing system. This method is then employed to average the dynamics over a lattice period for a nonlinear focusing system, provided by the use of higher order poles such as sextupoles and octupoles along with alternate gradient quadrupoles. Unlike the traditional approach, the higher order focusing is not treated as a perturbation. The Lie transform method is particularly advantageous for such a system where the form of the Hamiltonian is complex. This is because the method exploits the property of canonical invariance of Poisson brackets so that the change of variables is accomplished by just replacing the old ones with the new. The analysis shows the existence of a condition in which the system is azimuthally symmetric in the transformed, slowly oscillating frame. Such a symmetry in the time averaged frame renders the system nearly integrable in the laboratory frame. This condition leads to reduced chaos and improved confinement when compared to a system that is not close to integrability. Numerical calculations of single-particle trajectories and phase space projections of the dynamic aperture performed for a lattice with quadrupoles and sextupoles confirm that this is indeed the case.

A modified Boris-like integration, in which the spatial coordinate is the independent variable, is derived. This spatial-Boris integration method is useful for beam simulations, in which the independent variable is often the distance along the beam. The new integration method is second order accurate, requires only one force calculation per particle per step, and preserves conserved quantities more accurately over long distances than a Runge-Kutta integration scheme. Results from the spatial-Boris integration method and a Runge-Kutta scheme are compared for two simulations: (i) a particle in a uniform solenoid field and (ii) a particle in a sinusoidally varying solenoid field. In the uniform solenoid case, the spatial-Boris scheme is shown to perfectly conserve for any step size quantities such as the gyroradius and the perpendicular momentum. The Runge-Kutta integrator produces damping in these conserved quantities. In the sinusoidally varying case, the conserved quantity of canonical angular momentum is used to measure the accuracy of the two schemes. For the sinusoidally varying field simulations, error analysis is used to determine the integration distance beyond which the spatial-Boris integration method is more efficient than a fourth-order Runge-Kutta scheme. For beam physics applications where statistical quantities such as beam emittance are important, these results imply the spatial-Boris scheme is 3 times more efficient.

We present 2D simulations of both beam-driven and laser-driven plasma wakefield accelerators, using the object-oriented particle-in-cell code XOOPIC, which is time explicit, fully electromagnetic, and capable of running on massively parallel supercomputers. Simulations of laser-driven wakefields with low \(∼10¹⁶ W/cm²\) and high \(∼10¹⁸ W/cm²\) peak intensity laser pulses are conducted in slab geometry, showing agreement with theory and fluid simulations. Simulations of the E-157 beam wakefield experiment at the Stanford Linear Accelerator Center, in which a 30 GeV electron beam passes through 1 m of preionized lithium plasma, are conducted in cylindrical geometry, obtaining good agreement with previous work. We briefly describe some of the more significant modifications to XOOPIC required by this work, and summarize the issues relevant to modeling relativistic electron-neutral collisions in a particle-in-cell code.

A method for finding four-dimensional symplectic maps with an enlarged nearly integrable region is described. The method relies on solving for parameter values at which the linear stability factors of the fixed points (periodic orbits) of the map have the values corresponding to integer island tunes. This method is applied to accelerator lattices in order to increase dynamic aperture. The result shows a significant increase of the dynamic aperture after correction.

A method for reducing chaotic dynamics in four-dimensional symplectic maps is presented. The method is to reduce certain chaos measures related to the invariants of the tangent map of fixed points. This method is applied to circular accelerators, where chaotic dynamics determines the dynamic aperture, the region of long-time stable orbits. A factor of 3–4 increase in the phase-space volume of confined trajectories is obtained.

The criterion of approximate omnigeneity (i.e., having bounce-averaged drift lying within the magnetic surfaces) is much easier to satisfy than quasihelicity, the condition that B, the magnitude of the magnetic field, is a function of only a single linear combination of the toroidal angles. Simple criteria for omnigeneity are presented and used to construct exactly omnigenous forms for B that are far from quasihelical. Though this construction gives a nonanalytic function B, close to the constructed systems there exist other systems with analytic B. These results indicate that finding helical plasma confinement systems with minimal neoclassical transport is much easier than previously believed.

Particles interacting resonantly with large-amplitude coherent one-dimensional wave packets can trap and subsequently detrap or even reflect. Many resonant particles are strongly scattered in the process, and the long-time dynamics of such particles is stochastic throughout a large region of phase space when repeated wave-particle interactions occur. We apply adiabatic invariance theory and separatrix crossing theory to this Hamiltonian system, which is beyond the realm of quasilinear theory. We calculate the adiabatic invariant through first order in the (small) slowness parameter ɛ for all particle trajectories. Because the trajectories of resonant particles cross a separatrix, the adiabatic invariant is broken and separatrix-crossing theory must be used. Our Hamiltonian provides a simple model for the fundamental physics of narrow-spectrum plasma turbulence, for strong rf current drive in a tokamak, and for electron dynamics in a recirculating free-electron laser.

A method for creating integrable nonlinear accelerator lattices is presented. Fixed points for the two-dimensional return map corresponding to the lattice are found. Minimizing the residues (an indicator of the size of the associated island) of these fixed points by varying lattice parameters eliminates large islands and regions of chaos. The resulting nonlinear systems have larger dynamical apertures and are more stable to perturbations induced by, for example, error fields.

Quantum-mechanical evolution in a slowly varying double-well potential is analyzed in the semiclassical limit to determine the transition probability due to loss of adiabatic invariance of states having energy close to that of a separatrix in the equivalent classical system. Transformation to the rotating-axis basis reduces the problem to the integration of a set of coupled differential equations. In the adiabatic limit the integration is carried out by the method of successive approximations. For adiabatic parameter ε of the order of the inverse, 1/N, of the number of quantum states with energy below the separatrix, the spread of the quantum adiabatic invariant is exponentially small in the inverse of the adiabaticity parameter. Surprisingly, the transition to this quantum adiabatic behavior occurs far below the minimum transition frequency of the system.

Near-separatrix eigenfunctions for the double-well potential are analyzed. These functions are needed for the study of systems with perturbed or slowly varying double-well potentials. The probability density of separatrix eigenfunctions collapses to the classical result (a δ function at the unstable fixed point) logarithmically with the number of quantum states. Matrix elements with respect to this basis are also studied. Unlike the wave functions, the unnormalized matrix elements are nonsingular in the limit of large quantum number.

A new adiabatic theory permits the understanding of one-dimensional dynamics of particles interacting with a large-amplitude wave packet for bounce time short compared with the transit time. This theory differs from previous ones in that the Hamiltonian varies slowly not with the time, but with the coordinate. The resulting adiabatic invariant is not equal, even in lowest order, to the usual action. This theory predicts the basic features of the interaction observed in previous numerical studies.

The diffusion coefficient for particles in a field of randomly phased waves was calculated numerically. Spectra broad in wave number and broad in frequency exhibit identical behavior for the diffusion coefficient as a function of the overlap parameter ɛ. The diffusion coefficient exceeds the quasilinear value by a factor of about 2.5 at ɛ near 18. Differences greater than 25% between the two values exist far above the chaotic threshold (ɛ≊60). A mapping-based model with a small number of random phases qualitatively reproduces the results of the simulations.

The change of the crossing parameter (essentially the phase) between sequential slow separatrix crossings is calculated for Hamiltonian systems with one degree of freedom. Combined with the previous separatrix crossing analysis, these results reduce the dynamics of adiabatic systems with separatrices to a map. This map determines whether a trajectory leaving a given separatrix lobe is ultimately captured by the other lobe. Averaging these results over initial phase yields the reaction probability, which does not asymptote to the fully phase-mixed result even for arbitrarily long times between separatrix crossings.

A reply to he comment on quantum effects in a macroscopic system is prsented. (AIP)