1. Computational Modeling of Magnetic Intervention D. V. Rose*Voss Scientific, LLC A. E. Robson, J. D. Sethian, and J. L. Giuliani Naval Research Laboratory High Average Power Laser Program Workshop Naval Research Laboratory, Building 226 Auditorium October 30 and 31, 2007 *With a special acknowledgement to Chris Mostrom for continuing work on 3D graphics!

2. Status report on computational modeling for Magnetic Intervention (MI): • Electromagnetic analysis of the Pechacek experiment is essentially complete. • We are continuing to use this analysis to explore other computational models suitable for efficient EM analysis of IFE-scale MI physics. • Ion orbit analysis of the conventional MI concept has indicated that the escaping ion “beams” in both the ring and point cusps result in very high current densities. • No integrated, feasible solution of this ion-stopping/materials problem is known at this time. • Ion orbit analysis of the OCTACUSP MI concept (A. Robson) is underway (and is the main subject of this presentation): • Discussed in the previous presentation by A. Robson.

3. EMHD Simulation of “Pechacek” Experiment Complete: • The essential physical character of the experiment reproduced in a 2D, large-scale simulation. • This model is NOT directly extendable to IFE chamber-scale problems.

4. To “zeroth-order”, orbit calculations can be used to conduct relevant design studies for ions leaving the chamber: • We are continuing to develop new models that should lessen the discrepancies and handle the IFE chamber spatial & temporal scales. • The Pechacek experiment will continue to be the test case for all new algorithms. t (ms) t (ms)

5. EMHD vs Orbit Calculation: Ring cusp width and transverse velocities compared: Ion channel “width” as a function of time at r=29 cm in the escape cusp. Ion channel transverse momentum (vz) at r=29 cm.

6. Orbit Analysis of the “duckbill” dumps shows a narrow and sharply peaked ion deposition pattern: • The duckbill ion dump design does NOT look feasible for the ring cusp. • “5th” coil designs to spread the escaping ion ring have not been successful. HeliumDensity at25 ms

7. 5-coil design used to explore the energy separation of the ring-cusp ions: The resulting time-integratedenergy deposition is a littlebroader than the 4-coil case.

8. OCTACUSP Primary Coil Configurations Include: Triangles: Circles: Conformal Triangles:

9. |B| contour levels at z=0 plane illustrating magnetic void at center of trap (left). 3D representation of a single |B| iso-surface also shown (right). |B|~0.1T iso-surfaces The long tube-like extensions away from the center of the chamber at X-type neutral lines.

10. Magnetic topology of a single “tube” orX-type neutral line: Magnetic field at x=200 cm plane: Chamber wall, r=5 m

11. 3D view illustrates that the magnetic field lines extend through the eight solenoids: Sample streamlines withoutconductor boundaries: Sample streamlines withconductor boundaries:

12. 3D streamlines can aid in the analysis by looking for critical field line intercept points: “outside” view View from “inside” the chamber:

13. Sample Ion Orbit Calculation: • 5-meter radius vacuum chamber • Four triangular main “coils” mapped onto a 6-meter radius sphere • each triangle carrys 6 MA • Allows 1-meter for neutral shielding • Eight 1.1-meter radius solenoids along ion drift tubes • Drift tubes have an inner diameter of 0.9 meters • Solenoids composed of 11 individual rings, each carrying 100 kA • Only 3.0 MeV Helium ions (4He++) followed here. Oct17.lsp

14. Individual particle and density plots are less helpful here: Particle positions and densities at 5 ms:

15. Charge deposition on the chamber surfaces (time-integrated) is being used to optimize the magnetic field topology: Here, only surface cells with non-zerocharge deposition are plotted. All surface cells plotted

16. Views of the charge deposition in a single octant illustrate the three-fold symmetry in the escaping ion distribution For this case, about 40% of the ions reach theends of the drift tubes. About 2% are deposited at the neutral line points,and 58% are in the flowerpetals radiating out from the entrance to the drift tubes.

17. Target planes along the drift tubes are used to diagnose the escaping ion beams ( time-integrated). Lsp uses combinatorialgeometry of basic objectsto build physical spaces and material boundaries. Target planes alongone drift tube are shown.

18. 3D targets in drift tubes indicate a focused ion beam* At r = 10 m: * Additional diagnostics, not shown here, also indicate an expanding ion beam envelope.

19. Issues/Work-in-Progress: • Tapered X-type neutral line physics (including diamagnetic effects) needs to be addressed. • Full “Perkins” ion spectrum needs to be examined once the current design exercise is completed. • Lead vapor dE/dx mass-stopping analysis for the ions (realistic energy loading, radiation, thermal cycles, etc.). • The eight-fold symmetry of the OCTACUSP design adds complexity to the plasma/magnetic-field interaction analysis. (A full 3D inertialess-electron dynamic EM model is still being explored.)

20. Summary: • Issues with the “conventional” MI chamber (with 2 or 4 coil system with ring and point cusps) are forcing consideration of other magnetic field topologies. • Bertie’s OCTACUSP design: • preserves the spherical symmetry inherent in direct-drive systems • minimizes the chamber surface area for ion escape ports (~5%) • Other coil configurations are possible (nested triangles, etc.)

21. Backup slides:

22. Oct16.lsp 1-m radius solenoids at each point cusp, 2 kA/cm (11 rings each carrying x MA) 5-meter radius chamber Conformal Triangles on 6-m radius sphere, 3 MA 3 MeV He++ ion orbits followed Show magnetic field topology Ion orbits Sample density plot Energy deposition on surfaces.

23. Cutaway view of an iso-surface of |B| illustrates location of the neutral lines: |B|=0.6 T iso-surfaces. Neutral lines (6)lie along thecoordinate axesin this orientation,and terminatenear the chamberwall.

24. Plots of the ion charge deposition on conducting surfaces are used to guide the design of the magnetic fields. Ion Energy Delivery: ~20% in 8 tube ends ~4% in 6 neutral line points ~76% in the chamber wall (flower petals)

25. 3D targets in drift tubes indicate a focused ion beam* R = 6 m R = 10 m * Additional diagnostics, not shown here, also indicate an oscillating ion beam envelope.

26. Particle escape orbits are complex in the OCTACUSP magnetic field: Sample orbits for 3 MeVa particles launchedfrom the origin at differentinitial angles. Escape radius is 200 cm(the radius of the conductingspherical boundary).