*M. Reiser* `mreiser@glue.umd.edu`

3mm
*J. G. Wang* `jgwang@plasma.umd.edu`

Institute for Plasma Research

Univ. of Maryland

College Park, MD 20742, USA3mm

**1 Introduction**\

An active research program has been conducted in the Institute for Plasma Research, University of Maryland, to study the physics of space-charge dominated beams for advanced accelerator applications. We have been employing low energy (up to 10 keV), high perveance (up to 1.4 AV) electron beams in experiments to investigate the space-charge effects in beams. The main facility has been a 5-m long transport channel focused by 36 short solenoids. \

In the past our theoretical investigations of the collective effects in high current beams included the thermodynamic beam model, the emittance growth due to free energy (beam mismatch, etc.), the longitudinal instability, the image effect and geometry factor in bunched beams, etc. [1-7]\

In experiments on the transverse beam dynamics we launched a five-beamlet configuration and studied the emittance growth and halo formation due to charge homogenization and rms mismatch. [8-10] Comparison of the measurements with theoretical predictions and computer simulations showed excellent agreement. \

The longitudinal beam dynamics experiments involved pulse
compression and the propagation of space-charge waves.
We investigated the longitudinal particle distribution in
parabolic and rectangular bunches, the reconstruction of an
eroded rectangular bunch, the generation of single (fast or slow)
space-charge waves, the geometry factor due to perturbation in
space-charge dominated beams, and the reflection of space-charge
waves at bunched beam ends. [11-17]

**2 On-going experimental programs**\

There are three on-going experimental programs, namely, the experiment on the resistive-wall instability, the experiment on longitudinal energy spread, and the experiment on bending space-charge dominated beams. \

The resistive-wall instability experiment is performed in a transport channel made of a glass tube with resistive coating and a co-axial long solenoid for transverse focusing. Electron beams with localized perturbations are generated in a gridded electron gun and transported through the channel. The experiment has clearly demonstrated the growth of slow waves and the decay of fast waves. The growth/decay rates are measured in the long wavelength limit and are compared with theory. Good agreement has been found. [18,19] The experiment is still in progress to study the beam quality deterioration due to the instability; this entails the measurement of the longitudinal beam energy spread and transverse emittance associated with the perturbed particle distribution in both the fast and slow waves.\

The experiment on longitudinal energy spread has been performed to study the energy distribution along parabolic and rectangular bunches, and within localized space-charge waves. All of these measurements agree with theory. In addition, we are studying the longitudinal energy spread of a beam generated in a thermionic electron gun. Especially, we would like to see if and how relaxation of the temperature anisotropy () via Coulomb collisions (the Boersch effect) and collective mechanisms plays a role in increasing the energy spread. This research is in progress.\

In progress is also a new experiment to study the beam transport in a
printed-circuit-quadruple channel with bending elements.
This research is not only an essential part of our electron
ring project described in the next section, but also an
independent beam physics study. The goal of the experiment
is to investigate the possible energy spread and emittance
growth in bending of space-charge dominated beams. [20]

**3 Design and development of an electron recirculator**\

A major effort of our current research is the design and development of a small recirculator for the transport of a low-energy, highly space-charge dominated electron beam. [21] The ring will also provide a longer path for the study of beam dynamics than is available in our existing 5-m long transport channel. The major issues to be addressed with the ring include beam transport of currents considerably higher than the conventional tune-shift limit by fast resonance transversal in a small number of turns (100), equilibrium bunch profiles (parabolic, rectangular with ``ears''), bending and dispersion of space-charge dominated beams, behavior of localized space charge waves including bunch-end effects, longitudinal instability with induction modules, etc. An important goal of the electron ring experiments will be checking with theory and computer simulation codes.\

Figure shows the ring layout. A 10 keV, 100 mA, 30-75 ns electron beam from an electron gun will be injected into the ring (after transverse/longitudinal matching) with the aid of a pulsed, Panofsky-type quadruple system. The ring design is based on a ``wound-up'' linear FODO channel. Transverse focusing will be provided by 70 printed-circuit quadruples (plus two Panofsky quads of special design). Three induction/rf gaps will be used for longitudinal focusing. A pulsed extraction system similar to the injector will be included for beam analysis. Other diagnostics along the ring include fast beam position/current monitors, energy analyzers, and phosphor screen images. The ring main parameters are summarized in Table 1. The design of the ring is being developed with the collaboration of T. Godlove (FMT) and R. York (Michigan State University).

**Figure 3.1:** General layout of the electron recirculator

The University of Maryland proposed electron ring represents an exciting
opportunity to study the transport of highly space-charge dominated
beams. Potential applications are for circular accelerators requiring
intense pulses. These include high-energy physics booster synchrotrons,
muon colliders, spallation sources, drivers for heavy-ion inertial
fusion and free electron lasers.

**References**\

- 1.
- M. Reiser,
*Theory and Design of Charged Particle Beams*, John Wiley & Sons, Inc., New York, 1994. - 2.
- M. Reiser, ``Free Energy and Emittance Growth in Nonstationary
Charged Particle Beams'', J. Appl. Phys.
**70**, 1919 (1991). - 3.
- M. Reiser and N. Brown, ``Thermal Distribution of Relativistic
Particle Beams with Space Charge'', Phys. Rev. Lett.,
**71**(18), 2911 (1993) . - 4.
- M. Reiser and N. Brown, ``Proposed High-Current rf Linear
Accelerators with Beams in Thermal Equilibrium'', Phys. Rev. Lett.,
**74**(7), 1111 (1995). - 5.
- N. Brown and M. Reiser, ``Thermal Equilibrium of Bunched
Charged Particle Beams'', Physics of Plasmas
**2**(3), 965 (1995). - 6.
- J. G. Wang and M. Reiser, ``Longitudinal Instability of Space
Charge Dominated Beams in Transport Channels with Complex Wall
Impedances'', Physics Fluids B,
**5**(7), 2286 (1993). - 7.
- C. K. Allen, N. Brown, and M. Reiser, ``Image Effects for
Bunched Beams in Axisymmetric Systems'', Part. Accel.
**45**, 149 (1994). - 8.
- M. Reiser, C. R. Chang, D. Kehne, K. Low, T. Shea, H. Rudd,
and I. Haber, ``Emittance Growth and Image Formation in a Nonuniform
Space-Charge-Dominated Electron Beams'', Phys. Rev. Lett.
**61**, 2933 (1988). - 9.
- I. Haber, D. Kehne, M. Reiser and H. Rudd, ``Experimental,
Theoretical and Numerical Investigation of the Homogenization of
Density Nonuniformities in the Periodical Transport of a Space-Charge
Dominated Beam'', Phys. Rev. A
**44**, 5194 (1991). - 10.
- D. Kehne, K. Low, M. Reiser, T. Shea, C. R. Chang, and Y. Chen,
``Experimental Studies of Electron Beam Transport in the Maryland
Periodic Solenoid Channel'', Nucl. Inst. and Meth., A
**278**, 194 (1989). - 11.
- J. G. Wang, D. X. Wang, and M. Reiser, ``Longitudinal Expansion
of Space-Charge Dominated Drifting Beam Bunches with a Parabolic
Line Charge Density Distribution'', Appl. Phys. Lett.,
**62**(6), 645 (1993). - 12.
- D. X. Wang, J. G. Wang, D. Kehne, and M. Reiser, ``Experimental
Verification of a Longitudinal Beam-Envelope Model for a Space-Charge
Dominated Parabolic Bunch'', Appl. Phys. Lett.,
**62**(25), 3232 (1993). - 13.
- D. X. Wang, J. G. Wang, D. Kehne, M. Reiser, and I. Haber,
``Longitudinal Expansion and Compression of Electron Bunches with
Rectangular Line Charge Profiles'', Il Nuovo Cimento, Vol.
**106**A, N.11, 1739 (1993). - 14.
- D. X. Wang, J. G. Wang, and M. Reiser, ``Restoration of
Rectangular Pulse Shape after Edge Erosion for a Space-Charge
Dominated Electron Bunch'', Phys. Rev. Lett.,
**73**(1), 66 (1994). - 15.
- J. G. Wang, D. X. Wang, and M. Reiser, ``Generation of
Space-Charge Waves due to Localized Perturbations in a Space-Charge
Dominated Beam'', Phys. Rev. Lett.,
**71**(12), 1836 (1993). - 16.
- J. G. Wang, H. Suk, D. X. Wang, and M. Reiser, ``Determination
of the Geometry Factor for Longitudinal Perturbations in Space-Charge
Dominated Coasting Beams'', Phys. Rev. Lett.,
**72**(13), 2029 (1994). - 17.
- J. G. Wang, D. X. Wang, H, Suk, and M. Reiser, ``Reflection and
Transmission of Space-Charge Waves at the Ends of a Space-Charge
Dominated Electron Bunch'', Phys. Rev. Lett.,
**74**(16), 3153 (1995). - 18.
- H. Suk, J. G. Wang, and M. Reiser, ``Resistive-Wall Instability
Experiment in Space-Charge Dominated Electron Beams'', in the Proceedings
of the 1995 Particle Accelerator Conference and International Conference
on High-Energy Accelerators, Vol. 5, pp. 2974-2976, Dallas, Texas,
May 1-5, 1995.
- 19.
- J. G. Wang, H. Suk, and M. Reiser, ``Experimental Studies of
Space-Charge Waves and Resistive-Wall Instability in Space-Charge
Dominated Electron Beams'', to be published in Fusion Engineering and
Design.
- 20.
- S. Bernal, A. Dragt, M. Reiser, M. Venturini, J. G. Wang, and
T. Godlove, ``Injector and Matching Section Design for a Model Electron
Ring'', to be published in Fusion Engineering and Design.
- 21.
- M. Reiser, S. Bernal, A. Dragt, M. Venturini, J. G. Wang,
H. Onishi, and T. Godlove, ``Design Features of a Small Electron Ring
for Study of Recirculating Space-Charge Dominated Beams'',
to be published in Fusion Engineering and Design.

5mm