Overview of Heavy-Ion Fusion Focus on Computer Simulation Aspect*

Overview of Heavy-Ion Fusion Focus on computer simulation aspect*

Jean-Luc Vay

Heavy-Ion Fusion Virtual National Laboratory Lawrence Berkeley National Laboratory

Computer Engineering Science seminar University of California at Berkeley

February 4, 2003

*This work was performed under the auspices of the U.S. Department of Energy by the University of California, Lawrence Berkeley and Lawrence Livermore National Laboratories under Contract Numbers DE-AC03-76SF00098 and W-7405- Eng-48, and by the Princeton Plasma Physics Laboratory under Contract Number DE-AC02-76CH03073

The Heavy Ion Fusion Virtual National Laboratory The U.S. Heavy Ion Fusion Program - Participation

Lawrence Berkeley National Laboratory MIT Lawrence Livermore National Laboratory Advanced Ceramics Princeton Plasma Physics Laboratory Allied Signal Naval Research Laboratory National Arnold Los Alamos National Laboratory Hitachi Sandia National Laboratory Mission Research University of Maryland Georgia Tech University of Missouri General Atomic Stanford Linear Accelerator Center MRTI Advanced Magnet Laboratory Idaho National Environmental and Engineering Lab University of California a. Berkeley b. Los Angeles c. San Diego

Employees of LBNL, LLNL, and PPPL form the U.S. Virtual National Laboratory for Heavy Ion Fusion

The Heavy Ion Fusion Virtual National Laboratory Outline

Fusion energy – Principles, advantages/disadvantages – Basic requirements – Paths to fusion

Basic plasma computer models – Particle-In-Cell – Fluid

Heavy Ion Inertial Fusion – The target – The chamber – The accelerator

Conclusion

The Heavy Ion Fusion Virtual National Laboratory FUSION ENERGY

The Heavy Ion Fusion Virtual National Laboratory FUSION ENERGY: principles

The Heavy Ion Fusion Virtual National Laboratory Equivalence of mass and energy Example: Einstein’s equation if a 1 gram raisin was 2 converted completely into E = mc energy E = 1 gram x c2 -3 8 2 ± m = mass of particle = (10 kg) x (3.10 m/sec) = 9.1013 Joules 8 ± c = speed of light ~ 3.10 m/sec ~ 10,000 tons of TNT! huge amount of energy can be extracted from mass conversion.

Fusion

The Heavy Ion Fusion Virtual National Laboratory Advantages of fusion Virtually inexhaustible resources of fuel (water)

Clean (no CO2 emission, almost no radioactive waste) Fusion reactors are inherently safe. They cannot explode or overheat.

Byproducts or fuel cannot be used to build mass destruction weapons

The fuel is accessible worldwide

Disadvantages of fusion Complex, still at conceptual stage

Centralization of power sources

The Heavy Ion Fusion Virtual National Laboratory FUSION ENERGY: Basic requirements

The Heavy Ion Fusion Virtual National Laboratory Fundamental forces (some)

Holds

The Heavy Ion Fusion Virtual National Laboratory Potential barrier

In order to fuse, the nuclei have to overcome electrostatic barrier go into right direction

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-50 -40 -30 -20 -10 0 10 20 30 40 50 distance (arbitrary units) need energy (millions of degrees) need many events (many particles)

Find these conditions in?n “PLASMAS”

The Heavy Ion Fusion Virtual National Laboratory States of matter

The Heavy Ion Fusion Virtual National Laboratory FUSION ENERGY: Paths

The Heavy Ion Fusion Virtual National Laboratory The different paths to fusion energy

Far too big!

Tokamaks ITER

Lasers (NIF) Particle accelerators The Heavy Ion Fusion Virtual National Laboratory BASIC PLASMA COMPUTER MODELS

The Heavy Ion Fusion Virtual National Laboratory Computer simulation of plasmas

We compute on various platforms: pc (Pentium, Athlon), Pentium clusters, IBM-SP

IBM-SP very powerful parallel computer but need to simulate systems that contains at least 1000 billions of real particles

Even on the NERSC IBM-SP, the simulation of all the real particles is usually unfeasible

We have to make approximations!

The Heavy Ion Fusion Virtual National Laboratory Computer simulation of plasma as collection of particles

± We use macroparticles (1 macroparticle = many real particles) ± We compute the force (field) on a grid ± We advance particle and fields by finite time steps

δy δx The Heavy Ion Fusion Virtual National Laboratory Computer simulation of plasma as fluid

± A system containing many particles may (under certain conditions) be modeled as a fluid Example: air is made of molecules but is often described as a fluid ± Restriction: one location = one velocity

± We compute the fluid equation on a grid ± The temporal evolution of the fluid is computed using finite time steps

δy δx The Heavy Ion Fusion Virtual National Laboratory HEAVY ION INERTIAL FUSION

The Heavy Ion Fusion Virtual National Laboratory An Artist’s Conception of a Heavy Ion Fusion Power Plant

From the overall system, we identify several parts and study them separately using theory, experiments and computer simulations.

The Heavy Ion Fusion Virtual National Laboratory HEAVY ION INERTIAL FUSION: the target

The Heavy Ion Fusion Virtual National Laboratory For symmetric illumination, the target is enclosed into a capsule

Examples of capsule

“close coupled” “hybrid”

Hydrodynamic simulation of target implosion and capsule expansion (Lasnex)

The Heavy Ion Fusion Virtual National Laboratory LASNEX is validated against Laser fusion experiments

The Heavy Ion Fusion Virtual National Laboratory HEAVY ION INERTIAL FUSION: the chamber

The Heavy Ion Fusion Virtual National Laboratory Inside the chamber

(Lasnex simulation)

(Tsunami simulation)

The Heavy Ion Fusion Virtual National Laboratory Cut-away view shows beam and target injection paths for an example thick-liquid chamber

The Heavy Ion Fusion Virtual National Laboratory 3-D BPIC simulation of beam propagating through Flibe

beam ions Flibe ions electrons

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a e n a l p l a c o f n i y t i s n e t n c I n e i l F e HEAVY ION INERTIAL FUSION: the accelerator

The Heavy Ion Fusion Virtual National Laboratory Principles of particle accelerator (similar TV tube)

Acceleration

Transverse confinement Magnetic electric

≡

The Heavy Ion Fusion Virtual National Laboratory High Current Experiment (HCX) began operation January 11, 2002.

Marx ESQ injector matching diagnostics

10 ES quads

diagnostics

The Heavy Ion Fusion Virtual National Laboratory High-Current Experiment (HCX): first transport experiment using a driver-scale heavy-ion beam

K+, 1 - 1.8 MeV, 0.2 - 0.6 A, 4 - 10 µs, 10 - 40 ES quads HCX is to address four principal issues: ± Aperture limits (“fill factor”)? ± How maximum transportable current affected by misalignment, beam manipulations, and field nonlinearities ± beam halo? ± effects of gas and stray electrons? 9.44 m

2.51 m 3.11 m 2.22 m 1.38 m

K+ source end station ESQ injector Matching section 10 ES quads diagnostics HCX Transport: Transverse slice simulations with 3D applied fields and initial distributions from linked 3D injector simulations Goal: explore acceptable aperture fill factor

o At the end of the HCX Transport Channel o σ0= 80 σ0= 60 (smaller beam) (larger beam)

The Heavy Ion Fusion Virtual National Laboratory HEAVY ION INERTIAL FUSION: looking to the future

The Heavy Ion Fusion Virtual National Laboratory Near future - advanced multi-beam injector

Two possible ion source approaches

Use a large diameter but low current density single-aperture ion source. This is the traditional HIF approach.

4 mA/cm2

Extract hundreds of mm-scale high current density beamlets, from a multiple-aperture ion source.

100 mA/cm2/beamlet

Theory Simulation Experiment

The Heavy Ion Fusion Virtual National Laboratory Advanced multi-beam injector – planning first experiment

The Heavy Ion Fusion Virtual National Laboratory The future: Adaptive mesh refinement in WARP

Must resolve Debye length (fundamental plasma parameter) in beam ± mesh refinement offers a “better, cheaper, faster” field solution

The Heavy Ion Fusion Virtual National Laboratory Our next-step vision

Beam Science Inertial Fusion Energy

NOW (next three years) NEXT STEP

1.2 MV Preaccelerator using Einzel lens 0.4 MV beamlet- Brighter sources/ focusing for beamlets merging section

c m ESQ Channel

injector integrated beam experiment (IBX) - 1.0 m ¡ Maximum , n Transport Final Focus Source and injector Accelerator

Beam neutralization ...to test source-to-target- integrated modeling

Theory/simulations

The Heavy Ion Fusion Virtual National Laboratory 3 We will develop an integrated, detailed, and benchmarked source-to-target beam simulation capability

Ion source Accelerator Buncher Final Chamber Target & injector focus transport electrostatic / magnetoinductive PIC EM PIC rad - WARP LSP BPIC hydro

delta-f, continuum Vlasov, EM PIC delta-f BEST SLV LSP BEST

The Heavy Ion Fusion Virtual National Laboratory CONCLUSION

Fusion is a very attractive source of energy ± Would solve many problems ± But hard to achieve

Still far: there is lot of exciting science to study and technologies to develop

Computer simulation plays a crucial role in studying science, planning and analyzing experiments

The design of a full scale driver will rely heavily on integrated simulation from end-to-end

For more, visit our home page at http://hif.lbl.gov

The Heavy Ion Fusion Virtual National Laboratory MORE

The Heavy Ion Fusion Virtual National Laboratory Inertial Confinement Fusion Concept

Fuel Target Capsule Heating Compression Ignition Burn

A small metal Radiation Fuel is With the final Thermonuclear or plastic (light, X-rays, compressed driver pulse, burn spreads capsule ions, or (imploded) by the fuel core rapidly through (about the size electrons) rocket-like reaches about the compressed of a pea) rapidly heats blowoff 1000 times fuel, yielding contains the surface of (ablation) of liquid density many times the fusion fuel the fuel the surface and ignites at imput energy capsule material 100,000,000 degrees

Blowoff Radiation

The Heavy Ion Fusion Virtual National Laboratory Computer simulation of plasma: methods (3)

Vlasov ± Mathematically, the motion of a large collection of particles is equivalent to the motion of a fluid-like in a 6-D space (3-D space + 3-D velocities) we can solve using fluid representations

± The fluid is “discretized” on a 6-D grid ± The temporal evolution of the fluid is computed using finite time steps ± A lot less noisy than PIC but very expensive (interesting when very δ high accuracy is needed) vx δx The Heavy Ion Fusion Virtual National Laboratory SLV (Semi-Lagrangian Vlasov) simulation of beam in an anharmonic uniform focusing channel

Keep ƒ(x,v) at nodes of 4-D mesh; look back along orbits to obtain ƒ

Low-density and high-density regions of phase space are tracked equally well Black contour lines are 0.1, vx 0.01, 0.001, 0.0001, and 0.00001 of peak

Plan: generalize to alternating-gradient via sequential transforms x

The Heavy Ion Fusion Virtual National Laboratory Heavy Ion Fusion scheme diagram

ELECTRIC MAGNETIC INJECTOR FOCUS FOCUS CHAMBER ACCELERATOR ACCELERATOR FINAL FOCUS MATCHING POSSIBLE COMBINING PULSE BENDS COMPRESSION

The Heavy Ion Fusion Virtual National Laboratory LLNL is conducting neutronics analyses of final focus magnet shielding

± Magnet shielding calculations use 3-D representations of the chamber, flibe pocket, and magnet arrays

± Magnets are expected to last for over 30 years with adequate shielding

The Heavy Ion Fusion Virtual National Laboratory Chamber Transport Simulation (BIC)

No plasma 1013 cm-3 plasma

Plasma prevents beam deflection until z=200 cm where nb/np = 1

The Heavy Ion Fusion Virtual National Laboratory WARP3d simulation of 2 MV, 0.8 A electrostatic quadrupole injector

The Heavy Ion Fusion Virtual National Laboratory HCX effort is guided by simulations; here, we show a study of halo induced by beam envelope mismatch ε ε RMS emittance evolution x/ x,initial vs. beam fraction (32% mismatch amplitude) beam 1.2 fraction 100%

1.0 99%

This work established a 10% acceptable mismatch amplitude 0.8 90% for HCX 0 20 40 lattice periods Electrostatic Quadrupole

The Heavy Ion Fusion Virtual National Laboratory Simulation of multi-beamlet injector matching section

0.5 m 0.9 m

1.3 m 1.9 m

0.006 A, 91 beams, 1.200 MeV, 0.003 pi-mm-mrad S-G, 1024x1024, 1 cm/step, ratio of areas 0.070, beam size 0.800 mm 4.1 m 39.9 m