• E. Startsev, R.C. Davidson, H. Qin
  PPPL, Princeton, New Jersey

In electrically neutral plasmas with strongly anisotropic distribution functions, free energy is available to drive different collective instabilities such as the electrostatic Harris instability and the transverse electromagnetic Weibel instability. Such anisotropies develop naturally in particle accelerators and may lead to a detoriation of beam quality. We have generalized the analysis of the classical Harris and Weibel instabilities to the case of a one-component intense charged particle beam with anisotropic temperature including the important effects of finite transverse geometry and beam space-charge. For a long costing beam, the delta-f particle-in-cell code BEST and the eighenmode code bEASt have been used to determine detailed 3D stability properties over a wide range of temperature anisotropy and beam intensity. A theoretical model is developed which describes the essential features of the linear stage of these instabilities. Both, the simulations and analytical theory, clearly show that moderately intense beams are linearly unstable to short-wavelength perturbations, provided the ratio of the longitudinal temperature to the transverse temperature is smaller than some threshold value.

• H. Qin, R.C. Davidson
  PPPL, Princeton, New Jersey

Single-particle dynamics in a time-dependent focusing field is examined. The existence of the Courant-Snyder invariant* is fundamentally the result of the corresponding symmetry admitted by the oscillator equation with time-dependent frequency.** A careful analysis of the admitted symmetries reveals a deeper connection between the nonlinear envelope equation and the oscillator equation. A general theorem regarding the symmetries and invariants of the envelope equation, which includes the existence of the Courant-Snyder invariant as a special case, is demonstrated. The symmetries of the envelope equation enable a fast algorithm for finding matched solutions without using the conventional iterative shooting method.

*E.D. Courant and H.S. Snyder, Ann. Phys. 3, 1 (1958). **R.C. Davidson and H. Qin, Physics of Intense Charged Particle Beams in High Energy Accelerators (World Scientific, 2001).

• P. Efthimion, R.C. Davidson, E.P. Gilson, L. Grisham
  PPPL, Princeton, New Jersey
• B. G. Logan, W. Waldron, S. Yu
  LBNL, Berkeley, California

Plasmas are employed as a medium for charge neutralizing heavy ion beams to allow them to focus to a small spot size. Calculations suggest that plasma at a density of 1-100 times the ion beam density and at a length ~ 0.1-1 m would be suitable. To produce 1 meter plasma, large-volume plasma sources based upon ferroelectric ceramics are being considered. These sources have the advantage of being able to increase the length of the plasma and operate at low neutral pressures. The source will utilize the ferroelectric ceramic BaTiO3 to form metal plasma. The drift tube inner surface of the Neutralized Drift Compression Experiment (NDCX) will be covered with ceramic. High voltage (~ 1-5 kV) is applied between the drift tube and the front surface of the ceramic by placing a wire grid on the front surface. A prototype ferroelectric source 20 cm long produced plasma densities ~ 5x1011 cm-3. The source was integrated into the experiment and successfully charge neutralized the K ion beam. Presently, the 1 meter source is being fabricated. It will be characterized and integrated into NDCX for charge neutralization experiments. Experimental results will be presented.

• E.P. Gilson, M. Chung, R.C. Davidson, P. Efthimion, R. M. Majeski, E. Startsev
  PPPL, Princeton, New Jersey

The Paul Trap Simulator Experiment (PTSX) makes use of a compact Paul trap configuration with quadrupolar oscillating wall voltages to simulate the propagation of intense charged particle beams over distances of many kilometers through magnetic alternating-gradient transport systems. The simulation is possible because of the similarity between the transverse dynamics of particles in the two systems. One-component pure cesium ion plasmas have been trapped that correspond to normalized intensity parameters s < 0.8, where s is the ratio of the square of the plasma frequency to twice the square of the average transverse focusing frequency. The PTSX device confines the plasma for hundreds of milliseconds, which is equivalent to beam propagation over tens of kilometers. Results are presented for experiments in which the amplitude of the oscillating confining voltage waveform has been modified as a function of time. A comparison is made between abrupt changes in amplitude and adiabatic changes in amplitude. The effects of varying the frequency are also discussed. A barium ion source and a laser system have been installed and initial measurements made with this system are presented.

• A.B. Sefkow, R.C. Davidson, P. Efthimion, E.P. Gilson
  PPPL, Princeton, New Jersey
• F.M. Bieniosek, J.E. Coleman, S. Eylon, W.G. Greenway, E. Henestroza, J.W. Kwan, P.K. Roy, D.L. Vanecek, W. Waldron, S. Yu
  LBNL, Berkeley, California
• D.R. Welch
  ATK-MR, Albuquerque, New Mexico

Heavy ion drivers for high energy density physics applications and inertial fusion energy use space-charge-dominated beams which require longitudinal bunch compression in order to achieve sufficiently high beam intensity at the target. The Neutralized Drift Compression Experiment-1A (NDCX-1A) at Lawrence Berkeley National Laboratory (LBNL) is used to determine the effective limits of neutralized drift compression. NDCX-1A investigates the physics of longitudinal drift compression of an intense ion beam, achieved by imposing an initial velocity tilt on the drifting beam and neutralizing the beam's space-charge with background plasma. Accurately measuring the longitudinal compression of the beam pulse with high resolution is critical for NDCX-1A, and an understanding of the accessible parameter space is modeled using the LSP particle-in-cell (PIC) code. The design and preliminary experimental results for an ion beam probe which measures the total beam current at the focal plane as a function of time are summarized.

• E. Startsev, R.C. Davidson, W.L. Lee
  PPPL, Princeton, New Jersey

In intense charged particle beams with large energy anisotropy, free energy is available to drive transverse electromagnetic Weibel-type instabilities. Such slow-wave transverse electromagnetic instabilities can be described by the so-called Darwin model, which neglects the fast-wave portion of the displacement current. The Weibel instability may also lead to an increase in the longitudinal velocity spread, which would make the focusing of the beam difficult and impose a limit on the minimum spot size achievable in heavy ion fusion experiments. This paper reports the results of recent numerical studies of the Weibel instability using the Beam Eigenmode And Spectra (bEASt) code for space-charge-dominated, low-emittance beams with large tune depression. To study the nonlinear stage of the instability, the Darwin model is being developed and incorporated into the Beam Equilibrium Stability and Transport(BEST) code.

• J.J. Barnard, D. A. Callahan, A. Friedman, R.W. Lee, M. Tabak
  LLNL, Livermore, California
• R.J. Briggs
  SAIC, Alamo, California
• R.C. Davidson, L. Grisham
  PPPL, Princeton, New Jersey
• E. P. Lee, B. G. Logan, P. Santhanam, A. Sessler, J.W.  Staples, J.S. Wurtele, S. Yu
  LBNL, Berkeley, California
• C. L. Olson
  Sandia National Laboratories, Albuquerque, New Mexico
• D. Rose, D.R. Welch
  ATK-MR, Albuquerque, New Mexico

One approach to heat a target to "Warm Dense Matter" conditions (similar, for example, to the interiors of giant planets or certain stages in Inertial Confinement Fusion targets), is to use intense ion beams as the heating source. By consideration of ion beam phase space constraints, both at the injector, and at the final focus, and consideration of simple equations of state, approximate conditions at a target foil may be calculated. Thus target temperature and pressure may be calculated as a function of ion mass, ion energy, pulse duration, velocity tilt, and other accelerator parameters. We examine the variation in target performance as a function of various beam and accelerator parameters, in the context of several different accelerator concepts, recently proposed for WDM studies.

• M. Chung, R.C. Davidson, P. Efthimion, E.P. Gilson, R. M. Majeski, E. Startsev
  PPPL, Princeton, New Jersey

The Paul Trap Simulator Experiment (PTSX) is a cylindrical Paul trap whose purpose is to simulate the nonlinear dynamics of intense charged particle beam propagation in alternating-gradient magnetic transport systems. For the in-situ measurement of the transverse ion density profile in the PTSX device, which is essential for the study of beam mismatch and halo particle production, a laser-induced fluorescence diagnostic system is being developed. Instead of cesium, which has been used in the initial phase of the PTSX experiment, barium has been selected as the preferred ion for the laser-induced fluorescence diagnostic. The installation of the barium ion source and the characterization of the tunable dye laser system are discussed. The design of the collection optics with an intensified CCD camera system is also discussed. Finally, initial test results using the laser-induced fluorescence diagnostic will be presented.

• A. Friedman, J.J. Barnard, D. A. Callahan, G.J. Caporaso, D.P. Grote, R.W. Lee, S.D. Nelson, M. Tabak
  LLNL, Livermore, California
• R.J. Briggs
  SAIC, Alamo, California
• C.M. Celata, A. Faltens, E. Henestroza, E. P. Lee, M. Leitner, B. G. Logan, G. Penn, L. R. Reginato, A. Sessler, J.W.  Staples, W. Waldron, J.S. Wurtele, S. Yu
  LBNL, Berkeley, California
• R.C. Davidson, L. Grisham, I. Kaganovich
  PPPL, Princeton, New Jersey
• C. L. Olson, T. Renk
  Sandia National Laboratories, Albuquerque, New Mexico
• D. Rose, C.H. Thoma, D.R. Welch
  ATK-MR, Albuquerque, New Mexico

The Heavy Ion Fusion Virtual National Laboratory (HIF-VNL) is developing the intense ion beams needed to drive matter to the High Energy Density (HED) regimes required for Inertial Fusion Energy (IFE) and other applications. An interim goal is a facility for Warm Dense Matter (WDM) studies, wherein a target is heated volumetrically without being shocked, so that well-defined states of matter at 1 to 10 eV are generated within a diagnosable region. In the approach we are pursuing, low to medium mass ions with energies just above the Bragg peak are directed onto thin target "foils," which may in fact be foams or "steel wool" with mean densities 1% to 100% of solid. This approach complements that being pursued at GSI, wherein high-energy ion beams deposit a small fraction of their energy in a cylindrical target. We present the requirements for warm dense matter experiments, and describe suitable accelerator concepts, including novel broadband traveling wave pulse-line, drift-tube linac, RF, and single-gap approaches. We show how neutralized drift compression and final focus optics tolerant of large velocity spread can generate the necessarily compact focal spots in space and time.

• P.K. Roy, A. Anders, D. Baca, F.M. Bieniosek, J.E. Coleman, S. Eylon, W.G. Greenway, E. Henestroza, M. Leitner, B. G. Logan, D. Shuman, D.L. Vanecek, W. Waldron, S. Yu
  LBNL, Berkeley, California
• R.C. Davidson, P. Efthimion, E.P. Gilson, I. Kaganovich, A.B. Sefkow
  PPPL, Princeton, New Jersey
• D. Rose, C.H. Thoma, D.R. Welch
  ATK-MR, Albuquerque, New Mexico
• W.M. Sharp
  LLNL, Livermore, California

Ion beam neutralization and compression experiments are designed to determine the feasibility of using compressed high intensity ion beams for high energy density physics (HEDP) experiments and for inertial fusion power. To quantitatively ascertain the various mechanisms and methods for beam compression, the Neutralized Drift Compression Experiment (NDCX) facility is being constructed at Lawrence Berkeley National Laboratory (LBNL). In the first compression experiment, a 260 KeV, 25 mA, K+ ion beam of centimeters size is radially compressed to a mm size spot by neutralization in a meter-long plasma column and beam peak current is longitudinally compressed by an induction velocity tilt core. Instrumentation, preliminary results of the experiments, and practical limits of compression are presented. These include parameters such as emittance, degree of neutralization, velocity tilt time profile, and accuracy of measurements (fast and spatially high resolution diagnostic) are discussed.

• R.C. Davidson, S.R. Hudson, I. Kaganovich, H. Qin, E. Startsev
  PPPL, Princeton, New Jersey

In application of heavy ion beams to high energy density physics and fusion, background plasma is utilized to neutralize the beam space charge during drift compression and/or final focus of the ion beam. It is important to minimize the deleterious effects of collective instabilities on beam quality associated with beam-plasma interactions. Plasma electrons tend to neutralize both the space charge and current of the beam ions. It is shown that the presence of the return current greatly modifies the electromagnetic Weibel instability (also called the filamentation instability), i.e., the growth rate of the filamentation instability greatly increases if the background ions are much lighter than the beam ions and the plasma density is comparable to the ion beam density. This may preclude using underdense plasma of light gases in heavy ion beam applications. It is also shown that the return current may be subject to the fast electrostatic two-stream instability.

• I. Kaganovich, R.C. Davidson, E. Startsev
  PPPL, Princeton, New Jersey

Ion-atom ionization cross sections are needed in many applications employing the propagation of fast ions through matter. When experimental data or full-scale theoretical calculations are non-existent, approximate methods must be used. The most robust and easy-to-use approximations include the Born approximation of quantum mechanics and the quasi-classical approach utilizing classical mechanics together with the Bohr-Sommerfeld quantization rule.* The simplest method to extend the validity of both approaches is to combine them, i.e., use the two different approaches but only for the regions of impact parameters in which they are valid, and sum the results to obtain the total cross section. We have recently investigated theoretically and experimentally the stripping of more than 18 different pairs of projectile and target atoms in the range of 3-38 MeV/amu to study the range of validity of various approximations. The results of the modified approach agree better with the experimental data than either the Born approximation or the quasi-classical approach, applied separately.

*I. D. Kaganovich et al., "Formulary and scaling cross sections for ion-atom impact ionization," http://arxiv.org/abs/physics/0407140.

• I. Kaganovich, R.C. Davidson, E. Startsev
  PPPL, Princeton, New Jersey

Background plasma can be used as an effective neutralization scheme to transport and compress intense ion beam pulses, and the application of a solenoidal magnetic field allows additional control and focusing of the beam pulse. Ion beam pulse propagation in a background plasma immersed in an applied solenoidal magnetic field has been studied both analytically and numerically with three different particle-in-cell codes (LSP, OOPIC-Pro and EDPIC) to cross-check the validity of the results. Very good charge and current neutralization is observed for high values of the solenoidal magnetic field.* However, for intermediate values of the solenoidal magnetic field, current neutralization is a complex process, and a sizable self-magnetic field is generated at the head of the beam. Collective wave excitations are also generated ahead of the beam pulse.

*I. D. Kaganovich, E. A. Startsev and R. C. Davidson, Nuclear Instruments and Methods in Physics Research A, in press (2004).

• H. Qin, R.C. Davidson, S.R. Hudson, E. Startsev
  PPPL, Princeton, New Jersey

The collective effects in high-intensity 3D bunched beams are described self-consistently by the nonlinear Vlasov-Maxwell equations.* The nonlinear delta-f method,** a particle simulation method for solving the nonlinear Vlasov-Maxwell equations, is being used to study the collective effects in high-intensity 3D bunched beams. The delta-f method, as a nonlinear perturbative scheme, splits the distribution function into equilibrium and perturbed parts. The perturbed distribution function is represented as a weighted summation over discrete particles, where the particle orbits are advanced by equations of motion in the focusing field and self-consistent fields, and the particle weights are advanced by the coupling between the perturbed fields and the zero-order distribution function. The nonlinear delta-f method exhibits minimal noise and accuracy problems in comparison with standard particle-in-cell simulations. A self-consistent 3D kinetic equilibrium is first established for high intensity bunched beams. Then, the collective excitations of the equilibrium are systematically investigated using the nonlinear delta-f method implemented in the Beam Equilibrium Stability and Transport (BEST) code.

*R.C. Davidson and H. Qin, Physics of Intense Charged Particle Beams in High Energy Accelerators (World Scientific, 2001). **H. Qin, Physics of Plasmas 10, 2078 (2003).