Beam dynamics of NDCX-II, a novel pulse-compressing ion accelerator *

Beam dynamics of NDCX-II, a novel pulse-compressing ion accelerator *

* This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Security, LLC, Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344, by LBNL under Contract DE-AC02-05CH11231, and by PPPL under Contract DE-AC02-76CH03073.

The Heavy Ion Fusion Science Virtual National Laboratory

Alex Friedman

Fusion Energy Program, LLNLand

Heavy Ion Fusion Science Virtual National LaboratoryAPS Division of Plasma Physics Conference, Atlanta, November 2009

22

The Heavy Ion Fusion Science Virtual National Laboratory 2

This work was done in collaboration with others …

LLNL:

John Barnard, Ron Cohen, Dave Grote, Steve Lund, Bill Sharp

LBNL:

Andy Faltens, Enrique Henestroza, Jin-Young Jung, Joe Kwan, Ed Lee, Matthaeus Leitner, Grant Logan, Jean-Luc Vay, Will Waldron

PPPL:

Ron Davidson, Mikhail Dorf, Phil Efthimion, Erik Gilson, Igor Kaganovich

33


Outline

• Introduction to the project

• 1-D ASP code model and physics design

• Warp (R,Z) simulations

• 3-D effects: misalignments & corkscrew

• Status of the design

44


NDCX-II is under way !

DOE’s Office of Fusion Energy Sciences approved the NDCX-II project earlier this year.

$11 M of funding has been provided via the American Recovery and Reinvestment Act (“stimulus package”).

Construction of the initial 15-cell configuration began in July 2009, with completion planned for March 2012.

55


NDCX-II will enable studies of warm dense matter, and key physics for ion direct drive

LITHIUM ION BEAM BUNCH (ultimate goals)

Final beam energy: ~ 3 MeVFinal spot diameter : ~ 1 mmFinal bunch length : ~ 1 cm or ~ 1 nsTotal charge delivered: ~ 30 nC

Exiting beam available for measurement

TARGET

m foil or foam

30 J/cm2 isochoric heating would bring aluminum to ~ 1 eV

66


“Neutralized Drift Compression” produces a short pulse of ions

• The process is analogous to “chirped pulse amplification” in lasers• A head-to-tail velocity gradient (“tilt”) is imparted to the beam by one or

more induction cells• This causes the beam to shorten as it moves down the beam line:

• Space charge would inhibit this compression, so the beam is directed through a plasma which affords neutralization

• Simulations and theory (Voss Scientific, PPPL) showed that the plasma density must exceed the beam density for this to work well

z (beam frame)

vz

z (beam frame)

vz

77


NDCX-I at LBNL routinely achieves current and power amplifications exceeding 50x

NDCX-I

injectorbeam

transport solenoids

induction bunching module

final focus

solenoidtarget

chamber with

plasma sources

drift compression

line

88


LLNL has given the HIFS-VNL 48 induction cells from the ATA

• They provide short, high-voltage accelerating pulses–Ferrite core: 1.4 x 10-3 Volt-seconds–Blumlein: 200-250 kV; 70 ns FWHM

• At front end, longer pulses need custom voltage sources; < 100 kV for cost

Test stand at LBNL

Advanced Test Accelerator (ATA)

99


ATA induction cells with pulsed 1-3T solenoidsLength ~ 15 mAvg. 0.25 MV/mPeak 0.75 MV/m

Li+ ion injector

final focus and target chamber

neutralized drift compression line with plasma sources

water-filled Blumlein voltage sources

oil-filled transmission lines

NDCX-II(23-cell design)

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Outline






1111


1-D PIC code ASP (“Acceleration Schedule Program”)

• Follows (z,vz) phase space using a few hundred particles (“slices”)

• Accumulates line charge density (z) on a grid via particle-in-cell• Space-charge field via Poisson equation with finite-radius correction term

Here, α is between 0 (incompressible beam) and ½ (constant radius beam) • Acceleration gaps with longitudinally-extended fringing field

– Idealized waveforms– Circuit models including passive elements in “comp boxes”– Measured waveforms

• Centroid tracking for studying misalignment effects, steering• Optimization loops for waveforms & timings, dipole strengths (steering)• Interactive (Python language with Fortran for intensive parts)

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Physics design principle 1: Shorten Beam First (“non-neutral drift compression”)

• Equalize beam energy after injection -- then --

• Compress longitudinally before main acceleration

• Want < 70 ns transit time through gap (with fringe field) as soon as possible

==> can then use 200-kV pulses from ATA Blumleins

• Compress carefully to minimize effects of space charge

• Seek to achieve large velocity “tilt” vz(z) ~ linear in z “right away”

1313


Physics design principle 2: Let It Bounce

• Rapid inward motion in beam frame is required to get below 70 ns

• Space charge ultimately inhibits this compression

• However, so short a beam is not sustainable– Fields to control it can’t be “shaped” on that timescale– The beam “bounces” and starts to lengthen

• Fortunately, the beam still takes < 70 ns because it is now moving faster

• We allow it to lengthen while applying:– additional acceleration via flat pulses– confinement via ramped (“triangular”) pulses

• The final few gaps apply the “exit tilt” needed for neutralized drift compression

1414


Pulse length vs. z: the “bounce” is evident

puls

e le

ngth

(m

)

center of mass z position (m)

1515


Pulse duration vs. z

- time for entire beam to cross a plane at fixed z

* time for a single particle at mean energy to cross finite-length gap

+ time for entire beam to cross finite-length gap

puls

e du

ratio

n (n

s)

center of mass z position (m)

1616


Voltage waveforms for all gaps

“ramp” (using measured waveform from test stand)

“flat-top” (here idealized)

equalize beam energy after injection

“shaped” (to impose velocity tilt for initial compression)

gap

volta

ge (

kV)

time (µs)

1717


A series of snapshots from ASP shows the evolution of the (kinetic energy, z) phase space and current profile

1818


Outline






1919


Design of injector is done using Warp PIC code in (r,z) geometry

extractor111 kV

emitter130 kV

0

10 cm

First, use Warp’s steady-flow “gun” mode:

For full runs, use time-dependent space-charge-limited emission and simple mesh refinement

accel-50 kV

0 Z (m) 1

0

R (

m)

0

.1

decel0 V (during main pulse)

(2 mA/cm2 Li+ emission)

2020


ASP & Warp show reasonably good agreement (ASP is noisier)

Video: Warp (r,z) simulation of NDCX-II beam

2222


Outline






Video: Warp 3-D simulation of NDCX-II beam (no misalignments)

Video: Warp 3D simulation of NDCX-II, including random offsets of solenoid ends by up to 1 mm (0.5 mm is nominal)

2525


ASP employs a tuning algorithm (as in ETA-II, DARHT)† to adjust “steering” dipoles so as to minimize a penalty function

Head - redMid - greenTail – blue

x - solidy - dashed

Dipoles in every 4th solenoid;optimization penalizes corkscrew amplitude & beam offset, and limits dipole strength

Trajectories of head, mid, tail particles, and corkscrew amplitude, for a typical ASP run.Random offsets of solenoid ends up to 1 mm were assumed; the effect is linear.

Dipoles off

Corkscrew amplitude - black

†Y-J. Chen, Nucl. Instr. and Meth. A 398, 139 (1997).

2626


Outline






2727


The “physics design” is periodically updated, using several steps

① Use Warp to develop the diode and injector

② Capture particle data at a plane upstream of the first gap, import into ASP

③ Run ASP; optimize the machine “lattice” (drift spaces) & gap waveforms

④ Import lattice and waveforms into Warp, and in (r,z) geometry:

a) optimize solenoid strengths for a transversely “well-matched” beam

b) optimize final focusing solenoid for a small spot, with focal plane coincident with shortest pulse duration

⑤ Using the above solenoid strengths, use ASP to study beam steering

⑥ Using Warp in 3-D, assess effects of misalignments on focal intensity

⑦ Coming up: comprehensive simulations including all non-ideal effects, coupled with steering and other corrections

In some ways the process is analogous to fusion target design: we use simulations to develop shaped impulses that yield a desired compression

2828


Ferroelectric Plasma Source

Cathodic-ArcPlasma Source

Developed by PPPL

NDCX-II beam neutralization is based on NDCX-I experience

2929


Key technical issues are being addressed

• Li+ ion source current density – We have measured* 3 mA/cm2, but for NDCX-II assume 1 - 2 mA/cm2

• Pulsed solenoid effects– Volt-seconds of ferrite cores are reduced by return flux of solenoids– Eddy currents (mainly in end plates) dissipate energy, induce noise– We’ll use flux-channeling copper shells, and thinner end plates

• Solenoid misalignment effects– Steering reduces corkscrew but requires beam position measurement– If capacitive or magnetic BPM’s prove too noisy, we’ll use scintillators

or apertures

• Require “real” voltage waveforms– A good “ramp” has been measured, and is used in ASP and Warp runs – We’re developing shaping circuits for “flatter flat-tops”; will revise design

to use the measured waveform

*P. K. Roy, et al., paper B06.00014, presented earlier today

3030


We look forward to a novel and flexible research platform

• NDCX-II will be a unique ion-driven user facility for warm dense matter and IFE target physics studies.

• The machine will also allow beam dynamics experiments relevant to high-current fusion drivers.

• The baseline physics design makes efficient use of the ATA components through rapid beam compression and acceleration.

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Later in this meeting … presentations on the physics of ion beams warm dense matter HIF targets

Poster Session NP8, Wednesday, 9:30 AM in Grand Hall East

2 and 3: NDCX-I results

4, 5, and 110: NDCX-II studies

6 – 9: ion beam dynamics (neutral and non-neutral)

93 – 96: WDM and HIF targets

Oral Session T05, Thursday, 9:30 AM in Hanover CDE

2 (9:42 AM): John Perkins, “High gain high efficiency heavy-ion direct drive targets”

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Extras

3333


A simple passive circuit can generate a wide variety of waveforms

Waveforms generated for various component values:

charged line

induction cell & accelerating gap impedance

ATA “compen-sation box”

3434


Passive circuit elements inserted into “compensation boxes” attached to the induction cells can shape waveforms nicely

Nearly linear voltage ramp over ~ 60 ns

3535


The field model in ASP yields the correct long-wavelength limit

• For hard-edged beam of radius rb in pipe of radius rw , 1-D (radial) Poisson eqn gives:

• The axial electric field within the beam is:

• For a space-charge-dominated beam in a uniform transport line, /rb2 ≈ const.; find:

• For an emittance-dominated beam rb ≈ const.; average over beam cross-section, find:

• The ASP field equation limits to such a “g-factor” model when the k⊥2 term dominates

• In NDCX-II we have a space-charge-dominated beam, but we adjust the solenoid strengths to keep rb more nearly constant;

• In practice we tune α to obtain agreement with Warp results

3636


Warp

• 3-D and axisymmetric (r,z) models

• Electrostatic space charge and acceleration gap fields

• Time-dependent space-charge-limited emission

• Cut cells boundaries, AMR, large-timestep drift-Lorentz mover, …

• Interactive (Python language)

• Extensively benchmarked against experiments & analytic cases

3737


Frames from an (r,z) Warp simulation

3838


A series of snapshots from ASP shows the evolution of the (velocity, z) phase space and line charge density profile

3939


ASP simulation of NDCX-II with 0.5 mm random magnet offsets and tilts shows that the beam reaches the target without steering

Should pass acceptance test without any steering. For operation, “Tuning V” methods from ATA, DARHT will be used.

4040


Warp 3D simulations indicate slow degradation of the focus as misalignment of the solenoids increases

• Random offsets in x and y were imparted to the solenoid ends. • The offsets were chosen from a uniform distribution with a set maximum.

Energy deposited within 1 mm Peak deposition of the location of the peak

4141


“Tuning V” algorithm (modeled in ASP) adjusts “steering” dipole currents so as to minimize a penalty function at the next sensor

Head - redMid - greenTail – blueCorkscrew - black

x - solidy - dashed

Random offsets of solenoid ends up to 1 mm were assumed; the effect is linear.

Simple tuning-V reduces corkscrew but still has a large centroid error

x,y vs z trajectories of head, mid, tail particles and the corkscrew size for a typical ASP run

Before optimization

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Beam offset can be added to penalty, but care is needed


x - solidy - dashed

Resonance occurs between sensor spacing and centroid oscillation

Constraining the dipole strength to< 100 Gauss reduces the peak

4343


An ensemble of runs shows the same trends


x - solidy - dashed

The results are averages over 20 simulations with differing random offsets of solenoid ends up to 1 mm.

x,y vs z trajectories of head, mid, tail particles and the corkscrew amplitudeBefore optimization

Simple tuning-V algorithm reduces the corkscrew amplitude but does not reduce the centroid error

4444


The effects of penalizing the beam offset and dipole strength are clearer when an ensemble of runs is examined


x - solidy - dashed

Constraining the dipole strength to< 100 Gauss removes the peak

Resonance between sensor spacing and cyclotron oscillation spatial period

4545


Fluence at target plane is appropriate for WDM experiments

34-cell lattice produces 4.3-MeV beam with final radius less than 1 mm• emittance remains between 1-2 mm-mrad through lattice• radius fluctuates between 2-3 cm during acceleration

4646


NDCX-II represents a significant upgrade over NDCX-I

• Baseline for WDM experiments: 1-ns Li+ pulse (~ 2x1011 ions, 30 nC, 30 A)

• For experiments relevant to ion direct drive: require a longer pulse with a “ramped” kinetic energy, or a double pulse.

Ion (atomic number / mass of common isotope)

Linac voltage - MV

Ion energy - MeV

Beam energy

- J

Target pulse - ns

Range -microns

(in ..)

Energy density 1011J/m3

NDCX-I K+ (19 / 39) 0.35 0.35 0.001- 0.003

2-3 0.3/1.5 (in solid/ 20% Al)

0.04

to 0.06

NDCX-II Li+1 (3 / 7) or

Na+3 (11 / 23)

3.5 - 5

3.5 - 15

0.1 - 0.28

1-2 (or 5 w hydro)

7 - 4 (in solid

Al)

0.25 to 1

4747


NDCX-I vs NDCX-II

NDCX-I (now) NDCX-II (future)

Ion K+ (A=39) Li+ (A=7)

Ion energy 400 keV 3-4 MeV

Focal radius 1.5 - 3 mm 0.5 mm

Pulse duration 2 - 4 ns 0.5 - 1 ns

Current amplification ~ 60 x 300 - 500 x

Peak current ~ 2 A ~ 30 A

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Beam dynamics of NDCX-II, a novel pulse-compressing ion accelerator *

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