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Beam and Accelerator Physics

Increased dynamic aperature of nonlinear accelerator lattices
Dynamic aperture is defined as the volume in phase which follows particles that remain confined in particle accelerators. The quest to find conditions that improve the dynamic aperture is a field of active research in accelerator physics. One factor that limits the size of the dynamic aperture is nonlinearities which are naturally occurring or need to be introduced for various reasons. We have been able to derive a condition for improved dynamic aperture for nonlinear, alternate gradient transport systems using Lie-transform perturbation theory. To do this the motion of the charged particle is cannonically averaged over fast time scales. This simplifies the expression of the Hamiltonian enabling one to find a condition for improved integrability. Numerical calculations using a fourth order symplectic integrator confirm that this condition leads to reduced chaos and optimum dynamic aperture (see Figure 1).
	Figure 1.
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Advanced acceleration by strong gradients produced by laser plasma interaction
All-optical injection schemes have the goal of extracting particles from the plasma and placing them in the accelerating region of phase space that is created by a laser wake field. We have shown through performing one and two-dimensional particle-in-cell (PIC) simulations, that all-optical injection schemes proposed in the past fail in producing a single pulse electron beam. As a consequence, injection is ubiquitous. It occurs throughout the wake field forming a train of beamlets, and because of this, single, short, narrow-energy-spread, beams are not obtained. Fig. 1 follows electrons in x-v_x phase-space for the colliding injection scheme using three-pulses.
	Figure 1.
We clearly observed multiple beamlets being generated. We show that single beamlets can be obtained with a "cleanup pulse," as suggested by D. Umstadter where a second laser pulse follows the pump pulse with a specific amplitude and phase to absorb the wake field generated by the pump pulse. Using this scheme, we are able to obtain high quality, single beams as is shown in Fig. 2.
	Figure 2.
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Simulations of transverse halo generations
A major issue facing the functioning of high current accelerators is beam halo formation. High current accelerators find applications in heavy ion fusion, nuclear waste treatment, production of tritium, production of radio isotopes for medical use and spallation neutron sources. The halo is formed by a small intensity distribution of particles surrounding the core of the beam. When such particles drift far away from the characteristic width of the beam, their loss will lead to the production of residual radioactivity of the accelerating system. Analytic models by Gluckstern have shown that halos are formed by a period-2 resonance between a test particle and a breathing core that
	Figure 1.
drives these particles to large amplitudes of oscillation.
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Crystallization of beams
The cooling process and the thermodynamics of electron plasma are investigated in strongly magnetized limit where the gyroradius of the electron is small compared with the mean inter-particle spacing. In the limit, the transfer of longitudinal and transverse energy nearly vanishes. For such a plasma there is effectively an extra thermodynamic parameter, as the longitudinal and transverse energies are independently conserved. As a cooling process, we introduce microwave cooling to the strongly magnetized electron plasma. Unlike ion plasmas, electron plasma, which has no internal degree of freedom, cannot be cooled down below a heat bath temperature.
	Figure 1. Time evolution of the longitudinal temperature for N₁/N₀ = 0.2, applying the best cooling parameters whenever the profile starts asymptotic behavior.
However, the 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. A microwave tuned to a frequency below the gyrofrequency forces electrons moving towards the microwave to absorb a microwave photon. Simultaneously the electrons move up one in Landau state and then lose their longitudinal momentum. In this process, the longitudinal temperature of the electron plasma can be decreased. On the basis that the transverse temperature is below the Landau temperature of the plasma, we set up two level transition equations and then derive
	Figure 2. Time evolution of the microwave intensity required for N₁/N₀ = 0.2 with the best cooling parameters.
a Fokker-Planck equation from the two level equations. With an aid of a finite element method (FEM) code for the equation, the cooling times for several values of the magnetic field, the microwave cavity, and the relative detuning frequency from the gyrofrequency, are calculated. Consequently, the optimal values of microwave cavity and detuning frequency from the gyrofrequency, for longitudinal cooling of a strongly-magnetized electron plasma with microwave bath, have been found. Consequently, the optimal values of microwave cavity and detuning frequency from the gyrofrequency, for longitudinal cooling of a strongly-magnetized electron plasma with microwave bath, have been found. By applying the optimal values with appropriate microwave intensity, the best cooling can be obtained. For the electron plasma magnetized with 10T, the cooling time to the solid state is approximately 2 hours. In Fig. 1 and Fig. 2, the results of the cooling are shown.
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Jean Stewart, Department of Internal Audit, University of Colorado Waste fraud abuse University of Colorado Jean Stewart IA University of Colorado Jean Stewart