ESTS0288 EBQ.

1. NAME OR DESIGNATION OF PROGRAM:  EBQ., EBQ, space charge transport charged particles.

3. DESCRIPTION OF PROGRAM OR FUNCTION

EBQ simulates steady state problems involving space charge transport of charged particles in cylindrically symmetric devices. It was written specifically to follow high current beam particles where space charge is important in long distance flight in axially symmetric machines possessing external electric and magnetic fields. EBQ simultaneously tracks all trajectories so as to allow procedures for charge deposition based on inter-ray separations. The orbits are treated in Cartesian geometry (position and momentum) with z as the independent variable. Poisson's equation is solved in cylindrical geometry on an orthogonal rectangular mesh. EBQ can also handle problems involving  multiple ion species where the space charge from each must be included. Such problems arise in the design of ion sources where different charge and mass states are present.

4. METHOD OF SOLUTION

EBQ solves Laplace's equation in cylindrical geometry by relaxation using the modified Lieberman procedure to obtain the electrostatic potential. Then, the rays are tracked simultaneously using the local gradient of the potential to find the electric field from the electrodes. Space charge is calculated either by application of Gauss' Law or by the potential found from solution of Poisson's equation with a known charge distribution. After ordering the particles in ascending order, the current enclosed by a ray is used to find the radial electrical space charge field by Gauss' Law and the self-magnetic field by Ampere's Law. The inter-ray spacing is used to map the appropriate charge density field onto a lattice, which is used on the next cycle to find the space charge field in addition to the electrode field by solution of Poisson's equation. The axially symmetric external magnetic field is found from the local magnetic vector potential.
The next cycle is started by solving Poisson's equation. The rays are then reinitialized and simultaneous tracking performed with the  rays depositing charge on the lattice for use on the next cycle. This set of calculations is repeated until a predetermined number of cycles are completed or until the first moment of the particle distribution fails to change by a predetermined amount.

5. RESTRICTIONS ON THE COMPLEXITY OF THE PROBLEM

Maxima of -
   4000 boundary points
    300 potentials
    100 trajectories
Due to the simultaneous processing of all rays, no retrograde motion is allowed.

6. TYPICAL RUNNING TIME:

7. UNUSUAL FEATURES OF THE PROGRAM:

8. RELATED AND AUXILIARY PROGRAMS:

10. REFERENCES

- Arthur C. Paul:
  EBQ Code Transport of Space Charge Beams in Axially Symmetric
  Devices
  LBL-13241 (November 1987).
- EBQ, NESC No. 9614.VX11B, EBQ Edition B Tape Description and
  Implementation Information
  NESC Note 91-15 (November 19, 1990).

- Arthur C. Paul:
EBQ Code, Transport of Space Charge Beams in Axially
Symmetric Devices
LBL-13241 (November 1982)

11. MACHINE REQUIREMENTS:

13. OPERATING SYSTEM UNDER WHICH PROGRAM IS EXECUTED:  VMS.

14. OTHER PROGRAMMING OR OPERATING INFORMATION OR RESTRICTIONS:

15. NAME AND ESTABLISHMENT OF AUTHORS

          J.T. Borges and E. Sheena
          Lawrence Berkeley Laboratory

LBL-13241 (November 1982)