M. Dorf (LLNL) In collaboration with I. Kaganovich , E. Startsev , and R. C. Davidson (PPPL)

1. Collective Focusing of a Neutralized Intense Ion Beam Propagating Along a Weak Solenodial Magnetic Field • M. Dorf (LLNL) • In collaboration with • I. Kaganovich, E. Startsev, and R. C. Davidson (PPPL) DOE Plasma Science Center, Teleseminar, April 19, 2012 Heavy Ion Fusion Science Virtual National Laboratory This work was performed under the auspices of the U.S. Department of Energy by the Lawrence Livermore National Laboratory under contract DE-AC52-07NA27344, and by the Princeton Plasma Physics Laboratory under contract AC02-76CH-O3073 LLNL-PRES-635456

2. Motivation: Controlled Fusion W. Sharp et al, http://hif.lbl.gov/tutorial/assets/fallback/index.html 2

3. Inertial Confinement Fusion: Lasers Versus Ion Beams Present approach – Laser Driven ICF National Ignition Facility (LLNL, Livermore, CA) Promising alternative – Heavy Ion Fusion Why ion beams? High production efficiency and repetition rate High efficiency of energy delivery and deposition 3

4. Ion-Beam-Driven High Energy Density Physics Heavy Ion Fusion (Future) Warm Dense Matter Physics (Present) foil Presently accessible ρ-T regime Ib~1-10 A Itotal~100 kA τb~ 1 ns D-T ρ~1 g/cm3, T~0.1 ÷ 1 eV τb~ 10 ns corresponds to the interiors of giant planets and low-mass stars Eb ~ 0.1-1 MeV Eb ~ 10 GeV ρ~1000 g/cm3 T~ 10 KeV Ions: K+, Li+ Atomic mass ~ 200 Block scheme of an ion driver for high energy density physics ion source acceleration and transport neutralized compression final focusing target 4

5. Neutralized Drift Compression Experiment (NDCX) Heavy ion driver for Warm Dense Matter Experiments Built and operated at the Lawrence Berkeley National Laboratory 5

6. Neutralized Drift Compression Experiment (NDCX) Schematic of the NDCX-I experimental setup (LBNL) Final Focus Solenoid Target 8T Fringe magnetic fields Beam parameters at the target plane upgrade Li+ @ 3MeV (βb=0.03) K+ @ 300 keV (βb=0.004) NDCX-II Ib~30 A , rb~1 mm (nb~6∙1012 cm-3) Ib~2 A , rb < 5 mm (nb~1011 cm-3) Ttarget ~1 eV Ttarget ~0.1 eV Weak fringe magnetic fields (~100 G) penetrate deeply into the background plasma 6

7. Outline I. Enhanced self-focusing of an ion beam propagating through a background plasma along a weak (~100 G) solenodial magnetic field important for the design of a heavy-ion driver (e.g. NDCX neutralized drift section) can be utilized in ion beam self-pinch transport applications (e.g. HIF drivers) II. Collective Focusing (Robertson) Lens can be used for the ion beam final focus (e.g. NDCX-I, II) perhaps can be utilized for collimation of laser generated proton beams Collective focusing with B0 ~ 1 kG is equivalent to standard magnetic focusing with B0 ~10 T 7

8. I. Ion Beam Propagation through a Neutralizing Background Plasma Along a Solenoidal Magnetic Field plasma e- vb ion beam B0 8

9. Magnetic Self-Pinching (B0=0) The ion beam space-charge is typically well-neutralized What about ion beam current? e- r e- Inductive field accelerates electrons beam z e- e- λ=c/ωpe collisionless electron skin depth (np~1011 cm-3 → λ~1.7 cm) defines the characteristic length scale for screening current (or magnetic-field) perturbations in a cold plasma (“inductive” analog of the Debye length) Electron radial force balance Current neutralization Magnetic pinching is dominant 9

10. Enhanced Collective Self-Focusing (B0~100 G) Radial displacement of background electrons is accompanied by an azimuthal rotation Strong radial electric field is produced to balance the magnetic V×B force acting on the electrons for This radial electric field provides enhanced ion focusing There is a significant enhancement of the ion beam self-focusing effect in the presence of a weak solenoidal magnetic field (for rb<<c/ωpe) M. Dorf et al, PRL103, 075003 (2009). 10

11. Enhanced Self-Focusing is Demonstrated in Simulations Gaussian beam: rb=0.55c/ωpe, Lb=3.4rb, β=0.05, nb=0.14np, np=1010 cm-3 Radial electric field Radial focusing force LSP (PIC) Bext=300 G Central beam slice Beam density profile ωce/2βbωpe=9.35 R (cm) Fr/Zbe(V/cm) Analytic LSP (PIC) Bext=0 Bext=300 G The enhanced focusing is provided by a strong radial self-electric field Magnetic self-pinching Collective self-focusing Influence of the plasma-induced collective focusing on the ion beam dynamics in NDCX-I is negligible NDCX-II is comparable to the final focusing of an 8 T short solenoid 11

12. Local Plasma Response is Drastically Different for ωce>2βbωpe and ωce<2βbωpe Moderate magnetic field(ωce>2βbωpe) Weak magnetic field (ωce<2βbωpe) -eEr e- FV×B δr>0 e- δr<0 - - + + FV×B -eEr - + - - + + B0 B0 Veφ<0 Veφ>0 Beam charge is overcompensated Beam charge is under-neutralized Radial electric field is focusing Radial electric field is defocusing Diamagnetic plasma response Paramagnetic plasma response ωce=2βbωpe resonant excitation of large-amplitudewhistler waves B0=100G np=1011 cm-3, βb=0.05 M. Dorf et al, PoP 19, 056704 (2012). 12

13. Numerical Simulations Demonstrate Qualitatively Different Local Plasma Responses ωce>2βbωpe ωce<2βbωpe B0=300 G (ωce/βbωpe=18.7) B0=25 G (ωce/βbωpe=1.56) Radial electric field Radial electric field LSP (PIC) LSP (PIC) Focusing electric field Defocusing electric field Diamagnetic response (δBz<0) Paramagnetic response (δBz>0) rb=0.55c/ωpe, lb=3.4rb, β=0.05, nb=0.14np, np=1010 cm-3 13

14. Whistler Wave Excitation Transverse magnetic field PIC (LSP) Analytic Semi-analytic Analytical treatment of poles in the complex plane Numerical integration (FFT) assuming weak dissipation Magnetic pick-up loop βb=0.33, lb=10rb, rb=0.9∙c/ωpe, nb=0.05np, Bext=1600G, np=2.4∙1011cm-3 Schematic of the detected signal Strong wave-field excitation Analytic theory is in very good agreement with the PIC simulations Signal amplitude Strong wave excitation occurs at ωce/2βbωpe (supported by PIC simulations) Enhanced self-focusing (local fields) Wave-field excitations can be used for diagnostic purposes ωce/2βbωpe 1 beam velocity=phase velocity=group velocity M. Dorf et al, PoP17, 023103 (2010). 14

15. II. The Use of Weak Magnetic Fields for Final Beam Focusing Schematic of the present NDCX-I final focus section FFS drift section (8 Tesla) Challenges: Operate 8 T final focus solenoid Fill 8 T solenoid with a background plasma Can a weak magnetic lens be used for tight final beam focusing? 15

16. Magnetic Lens magnetic lens charged particle beam q, vb B0 Br -vφ vb vb × Br provides azimuthal rotation (vφ) v φ × B0 provides radial focusing Cyclotron frequency Conservation of canonical azimutal (angular) momentum Equation of motion centrifugal force V×B Lorentz force 16

17. Collective Focusing Lens magnetic lens neutralized ion beam e-, i+ B0 Collective Focusing Concept* Neutralized beam focusing Electron beam focusing Ion beam focusing e i i+e β=0.01 β=0.01 β=0.01 Le ~0.01mm Li ~ 10m Lc=(LeLi)1/2 ~ 1 cm B=500 G L=10 cm B=500 G L=10 cm B=500 G L=10 cm Collective Focusing Lens The use of a collective focusing lens reduces the required magnetic field by (mi/me)1/2 *S. Robertson, PRL48, 149 (1982) 17

18. Collective Focusing Lens (Cont’d) Electrons traversing the region of magnetic fringe fields acquire an azimuthal velocity of Strong ambipolar electric field is produced to balance the magnetic V×B force acting on the co-moving electrons Electric force V×B magnetic force Centrifugal force Conditions for collective focusing 1. Quasi-neutrality 3. No pre-formed plasma inside the lens 2. Small magnetic field perturbations 18

19. Collective Focusing Lens for a Heavy Ion Driver Final Focus Schematic of the present NDCX-I final focus section drift section FFS (FFS) The ion beam can extract neutralizing electrons from the drift section filled with plasma. The collective focusing concept can be utilized for final ion beamfocusing in NDCX. No need to fill the final focus solenoid (FFS) with a neutralizing plasma Magnetic field of the FFS can be decreased from 8 T to ~700 G 19

20. Numerical Simulations Demonstrate Tight Collective Final Focus for NDCX-I Plasma Tilt gap z=8 -11 Final Focus Solenoid (700 G) Conductivity model kinetic 2 cm beam 35 266 271 281 0 251 z (cm) I simulation II simulation Schematic of the NDCX-I simulation R-Z PIC (LSP) Beam injection parameters: K+ @ 320 keV, rb=1.6 cm, Ib=27 mA Tb=0.094 eV, Plasma parameters (for the simulation II) np=1011 cm-3, Te=3 eV Beam density @ focal plane Radial electric field inside the solenoid Beam current @ focal plane nb (cm-3) 0.2 6×1012 cm-3 2.0 0.15 1.5 Er (kV/cm) Ib (A) r (cm) 0.1 LSP (PIC) 1.0 Analytic 0.05 0.5 0 0.0 280 281 282 283 2565 2576 2585 2595 time (ns) z (cm) r (cm) M. Dorf et al, PoP18, 033106 (2011) 20

21. Conclusions magnetic lens plasma neutralized ion beam e- ion beam e-, i+ B0 B0 Even a weak magnetic field (several hundred gauss) can have a significant influence on neutralized ion beam transport. Self-focusing force can be significantly enhanced by application of a weak magnetic field (~100 G) for rb<<c/ωpe. For a given focal length the magnetic field required for a neutralized beam is smaller by a factor of (me/mi)1/2. Can be important for the design of a heavy-ion driver (e.g. NDCX) Can be utilized for the ion beam final focus (e.g. NDCX-I, II) Perhaps could be utilized for collimation of laser generated proton beams Can be utilized for self-pinch ion beam transport applications

22. Enhanced Self-Focusing VS Collective Lens magnetic lens neutralized ion beam e-, i+ plasma B0 e- ion beam B0 Enhanced self-focusing Collective Lens Non-linear force can effectively balance p~Tb n (important for self-pinch transport) Linear force (important for beam focusing) Conditions: np=1011 cm-3, βb=0.05 Conditions: ωce>>2βbωpe B0>100 G rb>1cm no plasma inside the lens In the limit of rb~rge and Zbnb~ne →Fself~Fcol 22