# Presentation: 467297

## Toward a physics design for NDCX-II, a next-step platform for ion beam-driven physics studies*A. Friedman, D. P. Grote, W. M. Sharp, LLNL E. Henestroza, M. Leitner, B. G. Logan, W. L. Waldron, LBNLEleventh US-Japan Workshop on Heavy Ion Fusion and High Energy Density Physics, December 19, 2008,  Livermore CA

- Toward a physics design for NDCX-II, a next-step platform for ion beam-driven physics studies*A. Friedman, D. P. Grote, W. M. Sharp,* LLNL* E. Henestroza, M. Leitner, B. G. Logan, W. L. Waldron, *LBNL*Eleventh US-Japan Workshop on Heavy Ion Fusion and High Energy Density Physics, December 19, 2008,  Livermore CA

- *This work was performed under the auspices of the Office of Fusion Energy Sciences, U.S. Department of Energy, by LLNL under Contract DE-AC52-07NA27344, and by LBNL under Contract      DE-AC02-05CH11231.

- Heavy Ion Fusion Science
- Virtual National Laboratory

## For Warm Dense Matter studies, the NDCX-II beam must be accelerated to 3-4 MeV and compressed to ~1 ns (~1 cm)

- LITHIUM ION BEAM BUNCH
- Final Beam Energy:	**3-4 MeV**
- Final Spot Size :	**~ 1 mm diameter**
- Total Charge Delivered: 	**30 nC**    (~ 2x1011 particles or Imax ~ 30 A)

- Exiting beam available
- for dE/dx measurement

- THIN TARGET

## 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

## At least 40 ATA cells are available for NDCX-II

- 30 ATA induction cells with pulsed 1-3T solenoids

- final energy correction
- induction cell

- 100mA, 500ns Li+ ion injector

- final focus and target chamber  with diagnostics

- neutralized drift compression region with plasma sources

- water-filled Blumleins

- oil-filled transmission lines

- Estimated cost: $6M
- (includes contingency)

## 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.

## ATA cells are in good condition and match NDCX-II needs well

- Cells will be refurbished with stronger, pulsed solenoids

- They provide short, high-voltage accelerating pulses:
- Ferrite core: 1.4 x 10-3 Volt-seconds
- Blumlein: 200-250 kV for 70 ns
- At front end, longer pulses need custom voltage sources; < 100 kV for cost

## NDCX-II uses an accel-decel injector in which the “einzel lens” effect provides transverse confinement

- ground

- +102 kV pulsed source                 +68 kV DC        -170 kV DC      solenoid
- 10 mA/cm2                       extraction electrode     accel electrode

## Some issues were resolved; favorable features emerged

- Issues:
- An accelerating gap must be “on” while any of the beam overlaps its extended fringe field
- To shorten the fringe, the 6.7-cm radius of the ATA beam pipe                   is reduced to 4.0 cm
- Some pulses must be “shaped” to combat space charge forces
- We’ll do this via inexpensive passive circuits
- Space is limited
- 30-cell design (20 Blumleins + 10 lower-voltage sources) fits easily
- Favorable features:
- Most of machine uses modular 5-cell “blocks”
- Induction cells can impart all or most of final ~8% velocity “tilt”
- Current of compressed beam varies weakly w/ target plane over ~40 cm

## 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”

## We are well on our way toward a physics design for NDCX-II

- Accel-decel injector produces a ~ 100 keV Li+ beam with ~ 67 mA flat-top
- Induction accelerates it to 3.5 MeV at 2 A
- The 500 ns beam is compressed to ~ 1 ns in just ~ 14 m
- From 1-D code:

-               (C/m)

- Ek
- (MeV)

- entering linac

- at focus

-                (C/m)

- 0.4

- 0.0

- 0.5                      1.0

- 2.0

- 0.0

- 13.5                      14.0

- z (m)

- z (m)

- Ek
- (MeV)

- 0.0

- 0.1

- 0

- 4

## Physics design effort relies on PIC codes

- 1-D PIC code that follows (z,vz)
- Poisson equation with transverse falloff (“HINJ model”) for space charge
-  g0 = 2 log (rpipe / rbeam0)                k2 = 4 / (g0 rbeam02)
- A few hundred particles
- Models gaps as extended fringing field (Ed Lee’s expression)
- Flat-top initial beam with parabolic ends, with parameters from a Warp run
- “Realistic” waveforms: flat-top,“triangles” from circuit equation,                                	and low-voltage shaped “ears” at front end
- Interactive (Python language)
- Warp
- 3-D and axisymmetric (r,z) models; (r,z) used so far
- Electrostatic space charge and accelerating gap fields
- Time-dependent space-charge-limited emission

## Principle 1: Shorten Beam First (“non-neutral drift compression”) 

- 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 velocity “tilt” vz(z) ~ linear in z “right away”

## 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 (m) vs. z of center-of-mass

## Pulse duration vs. z

## Voltage waveforms for all gaps

## A series of snapshots shows how the (Ek,z) phase space and the line charge density evolve

-           (C/m)

- Ek
- (MeV)

- entering linac

- mid-compression

- peak
- compression

- z (m)

- expanding

- exiting

- at focus

## Video: line charge density and kinetic energy profiles vs. time

## We use the Warp code to simulate the NDCX-II beam in (r,z)

- 500 ns                            1500 ns                              2500 ns

- 3500 ns                            3835 ns                            3855 ns

- Transverse emittance growth (phase space dilution) is minimal

## Preliminary Warp (r,z) beam-on-target is encouraging; transverse dynamics and focusing optics design is still at an early stage

- Longitudinally: the goal is achieved; most of the beam’s 0.1 J passes through the target plane in ~1.2 ns

- Transversely: peak fluence of 17 J/cm2 is less than the 30 J/cm2 desired;   78% of beam falls within a 1 mm spot

## 1-D code (top) & Warp (bottom) results agree, with differences

-           (C/m)

- Ek
- (MeV)

- z (m)

-     1680 ns                                   2580 ns                                  2880 ns

-           (C/m)

- Ek
- (MeV)

- z (m)

## We look forward to a novel and flexible research platform

- The design concept is compact and attractive
- It applies rapid bunch compression and acceleration
- It makes maximal use of ATA induction modules and pulsed power
- Beam emittance is well preserved in simulations
- ... but considerable work remains before this is a true “physics design”
- NDCX-II will be able to deliver far greater beam energy and peak power for Warm Dense Matter physics than NDCX-I
- We will soon begin to develop an NDCX-II acceleration schedule that delivers a ramped-energy beam, for energy coupling and hydrodynamics studies relevant to direct-drive Heavy Ion Fusion

## Extras

## Progress has been encouraging; much remains to be done

- Proper accounting for initial beam-end energy variation due to space charge      (the 1-D run shown was initiated with a fully-formed uniform-energy beam)
- Other 1-D runs used a “model” initial energy variation and an entry “ear” cell; they produced compressed beams similar to the one shown
- However, that variation was not realistic; a Warp run using the 1-D-derived waveforms yielded inferior compression
- Better understanding of beam-end wrap-around (causes and consequences)
- A prescription for setting solenoid strengths to yield a well-matched beam
- Optimized final focusing, accounting for dependence of the focal spot upon velocity tilt, focusing angle, and chromatic aberration
- Assessment of time-dependent focusing to correct for chromatic effects
- Development of plasma injection & control for neutralized compression & focusing (schemes other than the existing FCAPS may prove superior)
- Establishment of tolerances for waveforms and alignment

- Major goals remain:
- a self-consistent source-through-target design, including assessment of tolerances etc., for WDM studies
- a prescription for modifications offering multiple pulses, ramped energy, and/or greater total energy, for ion direct drive studies

## These snapshots show how the (vz,z) phase space and the line charge density evolve (note the auto-scaling)

- These snapshots show how the (vz,z) phase space and the line charge density evolve (note the auto-scaling)

-           (C/m)

- vz
- (m/s)

- entering
- linac

- mid-
- compression

- peak
- compression

- z (m)

- expanding

- exiting

- at focus

- 13.78              13.80

- t = 3118 ns

## Simulations of NDCX-II neutralized compression and focus suggest that a plasma of density ~ 1014 cm-3 is desirable

- Simulations of NDCX-II neutralized compression and focus suggest that a plasma of density ~ 1014 cm-3 is desirable

- Idealized beam, uniform plasma, so far:
- Li+, 2.8 MeV, 1.67 eV temperature
- 2-cm -5 or -6.7 mrad convergence
- uniform current density;  = 24 mm-mrad
- 0.7-A with parabolic 50-ns profile
- applying ideal tilt for 30 ns of beam
- 1⁄2 mm 1-ns beam has 2x1013 cm-3 density

-  (LSP runs by D. Welch; others by A. Sefkow, M. Dorf; Warp code starting to be used)

- Radius

## We simulate injection from Cathodic-Arc Plasma sources

- 1.2 ns                                                         4.5 ns

- This run corresponds to an NDCX-I configuration with 4 sources
- It was made by Dave Grote using Warp in 3-D mode
- LSP has been used extensively for such studies