Beam dynamics of ndcx ii a novel pulse compressing ion accelerator
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Beam dynamics of NDCX-II, a novel pulse-compressing ion accelerator *. Alex Friedman Fusion Energy Program, LLNL and Heavy Ion Fusion Science Virtual National Laboratory APS Division of Plasma Physics Conference, Atlanta, November 2009.

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Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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

Alex Friedman

Fusion Energy Program, LLNL

and

Heavy Ion Fusion Science Virtual National Laboratory

APS Division of Plasma Physics Conference, Atlanta, November 2009

The Heavy Ion Fusion Science Virtual National Laboratory

* 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.


This work was done in collaboration with others

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


Outline

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


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”).

NDCX-II is under way !

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


Ndcx ii will enable studies of warm dense matter and key physics for ion direct drive

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 MeV

Final spot diameter :~ 1 mm

Final bunch length :~ 1 cm or ~ 1 ns

Total charge delivered: ~ 30 nC

TARGET

mm foil or foam

Exiting beam available for measurement

30 J/cm2 isochoric heating

would bring aluminum to ~ 1 eV


Neutralized drift compression produces a short pulse of ions

“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:

vz

z (beam frame)

vz

z (beam frame)

  • 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


Ndcx i at lbnl routinely achieves current and power amplifications exceeding 50x

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

beam transport solenoids

induction bunching module

drift compression line

final focus solenoid

injector

target chamber with plasma sources

NDCX-I


Llnl has given the hifs vnl 48 induction cells from the ata

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

Advanced Test Accelerator (ATA)

Test stand at LBNL


Ndcx ii 23 cell design

NDCX-II(23-cell design)

water-filled Blumlein voltage sources

Li+ ion injector

oil-filled transmission lines

ATA induction cells with pulsed 1-3T solenoids

Length ~ 15 m

Avg. 0.25 MV/m

Peak 0.75 MV/m

neutralized drift compression line with plasma sources

final focus and target chamber


Outline1

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


1 d pic code asp acceleration schedule program

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

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

Accumulates line charge density l(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)


Physics design principle 1 shorten beam first non neutral drift compression

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”


Physics design principle 2 let it bounce

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


Pulse length vs z the bounce is evident

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

pulse length (m)

center of mass z position (m)


Pulse duration vs z

Pulse duration vs. z

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

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

+time for entire beam to crossfinite-length gap

pulse duration (ns)

center of mass z position (m)


Voltage waveforms for all gaps

Voltage waveforms for all gaps

“flat-top” (here idealized)

“ramp” (using measured waveform from test stand)

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

gap voltage (kV)

equalize beam energy after injection

time (µs)


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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


Outline2

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


Design of injector is done using warp pic code in r z geometry

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

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

emitter

130 kV

extractor

111 kV

accel

-50 kV

decel

0 V

(during main pulse)

0 R (m) 0.1

10 cm

0

0 Z (m) 1

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

(2 mA/cm2 Li+ emission)


Asp warp show reasonably good agreement asp is noisier

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


Video warp r z simulation of ndcx ii beam

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


Outline3

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


Video warp 3 d simulation of ndcx ii beam no misalignments

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


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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

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 in every 4th solenoid;

optimization penalizes corkscrew amplitude & beam offset, and limits dipole strength

Dipoles off

x - solid

y - dashed

Corkscrew amplitude - black

Head - red

Mid - green

Tail – blue

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


Outline4

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


The physics design is periodically updated using several steps

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

  • Use Warp to develop the diode and injector

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

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

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

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

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

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

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

  • 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


Ndcx ii beam neutralization is based on ndcx i experience

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

Ferroelectric Plasma Source

Developed by PPPL

Cathodic-Arc

Plasma Source


Key technical issues are being addressed

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


We look forward to a novel and flexible research platform

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.


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

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”


Extras

Extras


A simple passive circuit can generate a wide variety of waveforms

A simple passive circuit can generate a wide variety of waveforms

Waveforms generated for various component values:

charged line

ATA “compen-sation box”

induction cell & accelerating gap impedance


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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

Nearly linear voltage ramp over ~ 60 ns


The field model in asp yields the correct long wavelength limit

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, l/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


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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


Frames from an r z warp simulation

Frames from an (r,z) Warp simulation


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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.


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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

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

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

Before optimization

x - solid

y - dashed

Head - red

Mid - green

Tail – blue

Corkscrew - black

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


Beam offset can be added to penalty but care is needed

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

Resonance occurs between sensor spacing and centroid oscillation

Constraining the dipole strength to< 100 Gauss reduces the peak

Head - red

Mid - green

Tail – blue

Corkscrew - black

x - solid

y - dashed


An ensemble of runs shows the same trends

An ensemble of runs shows the same trends

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

Before optimization

Head - red

Mid - green

Tail – blue

Corkscrew - black

x - solid

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

y - dashed

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


Beam dynamics of ndcx ii a novel pulse compressing ion accelerator

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

Resonance between sensor spacing and cyclotron oscillation spatial period

Constraining the dipole strength to< 100 Gauss removes the peak

Head - red

Mid - green

Tail – blue

Corkscrew - black

x - solid

y - dashed


Fluence at target plane is appropriate for wdm experiments

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


Ndcx ii represents a significant upgrade over ndcx i

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.


Ndcx i vs ndcx ii

NDCX-I vs NDCX-II


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