Simulation and Off-line Testing of a Square-wave- driven RFQ Cooler and Buncher for TITAN Mathew Smith: UBC/TRIUMF ISAC Seminar 2005.

Simulation and Off-line Testing of a Square-wave-driven RFQ Cooler and Buncher for TITAN

Mathew Smith: UBC/TRIUMFISAC Seminar 2005

Overview

The TITAN project

The need for a cooler and buncher

Square-wave vs sine-wave

Simulations

RFQ test stand

Experimental setup and status

Summary and outlook

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

magnetron (-) cyclotron (+)

axial (z)

B

U 0

z

Magnetron motion, ω-, due to magnetic field

Axial motion, ωz, due to application of an electrostatic harmonic potentialReduced cyclotron motion, ω+, due to coupling of ions magnetic moment to the electric field

Bm

qc

zc

2222

Dipole excitation prepares ions in pure ω- stateApplication of quadrupolar excitation couples ω- to ω+.

Extracting ions through magnetic field converts radial energy into longitudinal energyIon time of flight spectrum can be used to obtain ωc.

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

B

M C P

z

DRIFT TUBETRAP

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

TBNq

m

m

δm

dmm

O b se rva tio n Tim e (s)

1x10 -9

2x10 -9

5x10 -9

5x10 -8

1x10 -8

2x10 -8

1x10 -7

2x10 -7

0.01 0.015 0.02 0.03 0.05 0.07 0.1

B = 4 T, q = 1B = 6 T, q = 1B = 9.4 T, q = 1

m = 100 u, N = 10, 000

ISOLTRAP: t1/2 = 1 s, δm/m = 1x10-8

t1/2 = 50 ms, δm/m = 5x10-8

dmm

O b se rva tio n Tim e (s)

1x10 -9

2x10 -9

5x10 -9

5x10 -8

1x10 -8

2x10 -8

1x10 -7

2x10 -7

0.01 0.015 0.02 0.03 0.05 0.07 0.1

B = 4 T, q = 1B = 6 T, q = 1B = 9.4 T, q = 1

B = 4 T, q = 10

B = 4 T, q = 20B = 4 T, q = 30B = 4 T, q = 50

m = 100 u, N = 10, 000

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

TITAN: t1/2 = 50 ms, δm/m = 1x10-8 TBNq

m

m

δm

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Weak interaction studies

Atomic and Nuclear Mass Models

Stellar Nucleosynthesis

Motivation for mass measurements

Three areas where TITAN can contribute:

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Vud from mean Ft value and muon decay strength:

Q-Values needed for superallowed 0+->0+ beta emitters with A > 54Combined with half-lives and branching ratios this will help extend the number of well known Ft values

Weak Interaction Studies2 2 2 0.9967 0.0014ud us ubV V V

e.g. 74Rb, t1/2 = 50 ms, required δm/m = 1x10-8 current δm/m = 5x10-8.

0.9738 0.0004udV

b

s

d

VVV

VVV

VVV

b

s

d

tbtstd

cbcscd

ubusud

w

w

w

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Vud from average Ft value and muon decay strength:

Q-Values needed for superallowed 0+->0+ beta emitters with A > 54Combined with half-lives and branching ratios this will help extend the number of well known Ft values

Weak Interaction Studies2 2 2 0.9967 0.0014ud us ubV V V

e.g. 74Rb, t1/2 = 50 ms, required δm/m = 1x10-8 current δm/m = 5x10-8.

0.9738 0.0004udV

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Atomic and Nuclear Mass Models

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Production of all the heavy elements (A ≥ 7) take place via nuclear reactions in the stars In order to understand the complex chains of nuclear reactions that can take place inside a star (e.g. the s-, p-, r- and the rp- processes) it is necessary to know the masses of the nuclei involved Such chains involve a large number of short-lived nuclei which lie close to the proton and neutron drip lines

Stellar Nucleosynthesis

Be--beam

axially: electron beam space charge

50

m

trap potential Ut 450 V

longitudinally: electrodes

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

V

Io n B e a m

EBIT cannot accept a continuous beam

Low emittance needed in order to traverse magnetic field efficiently

Therefore, we need to cool and bunch the ISAC beam

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Standard quadrupolar geometry focuses in one direction and defocuses in the other

2 2

20

( )x yV

r

20

2,x

VE x

r 2

0

2y

VE y

r

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

However, it has long been known that by placing a series of quadrupoles together a net focusing force can be obtained

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Alternatively, we can use RF- potential to alternate the orientation of the focusing and defocusing directions

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

By segmenting the structure we can also apply a longitudinal field and hence create bunches

Thermalization of ion beam via interaction with a buffer gasThermalization in three dimensions leads to loss of beamCounter longitudinal energy loss via the application of an accelerating electric fieldIons disperse radially due to scattering of forward momentumUse RFQ ion trap to provide a force to counteract the dispersionHence, a gas-filled RFQ can be used to cool an ion beam

ISAC ion beam

RFQ cooler & buncher

EBIT chargebreeder

Penning trap

m/q selection

Sine-Wave Vs Square Wave: What is required?

The magnitude of V determines the depth of the psuedopotentialThis determines the traps acceptance, its transfer efficiency and its space-charge limit. Thus, it is desirable to have V as large as possibleIf V is fixed ω must be able to vary in order to trap a wide range of masses7 ≤ m ≤ 235 u, 0.4 ≤ f ≤ 3 MHz @ 400 Vpp, r0 = 10 mm

2 20

4,

zeVq

m r

Sine-Wave q<0.908 Stable, q≈0.4 best.

Square-Wave q<0.712 Stable, q≈0.3 best.

Inductor has limited bandwidthDriving off resonance causes core to heat up distorting induced waveHowever, used in all other experimental systems so the technology is proven

Experimental Viability: Sine Wave

Experimental Viability: Square-Wave

No lower limit on frequency, upper limit determined by energy dissipation in MOSFETs

Energy dissipation is determined by the capacitance of the RFQSystems have previously been developed that can run at up to Vpp

= 1 kV at up to 1 MhzHowever, these have only been use to drive 3-d Paul traps or small quadrupole mass filters, C ≈ 25 pFThe RFQ required for TITAN is significantly larger than a 3-d trap and has capacitance on the order of C ≈ 1500 pFSquare-Wave not possible with current MOSFETs?

Experimental Viability: Square-Wave

KICKER group at TRIUMF already had the solution to the capacitance problemBy stacking MOSFETs it is possible to reduce the energy dissipated by each chipFirst system designed and tested Vpp = 400V, f = 1 MHz (m ≥ 65)Improvements underway to try and expand to Vpp = 800 V, f = 3 MHzOther benefits include: equations of motion simpler than sinusoidal case, possibility to use frequency scanning methods or varying duty cycle to filter impurities

Experimental Viability: Square-Wave

The Square-Wave Driver

The Square-Wave Driver

Properties of the RFQ from Analytic Considerations

Meissner equations determine ions motion in square-wave-driven trap:

Analytic solution shows a simple harmonic macro-motion perturbed by a coherent micro-motionAs q increases so does the amplitude of the micro-motion until at q = 0.712 the motion becomes unbound

2

22 0,

xqx

2

22 0,

yqy

.2

t

Properties of the RFQ from Analytic Considerations

In Phase Spaceq = 0.3

Micro-motion distorts ideal harmonic ellipseAcceptance defined as area of harmonic ellipse whose maximum distorted amplitude = r0

Acceptance varies as a function of q with a maximum at q ≈ 0.3

TemperatureMicro-motion is coherent and therefore doesn’t contribute to the temperature of the ions in the trapTemperature of an ion cloud in a harmonic potential can be defined in terms of the standard deviation in position and momentum space:

Can use information from ellipses to convert from σx and σv as a function of phase/time to σx-SHM and σv-SHM and hence define temperature

1,u

s

kT

m

.v mkT

Space-Charge LimitCan use amplitude of harmonic motion combined with secular frequency to define the depth of the psuedopotentialUse simple model for the beam to get an idea of the space charge limitIn continuous mode consider beam to be an infinitely long cylinderIn bunched mode consider bunch to be a perfect sphere

2maxps s

mE r

ze

For Cylinder:

204sc

QE

R

For Sphere:

d

I

V

0

,2scE r

Space Charge LimitContinuous, Vd = 1000 m/s Bunched, t = 1 ms

In continuous mode Imax ≈ 2 μA, @ q = 0.39

In bunched mode Imax ≈ 30 nA, @ q = 0.33

Modeling Buffer-gas Cooling:Viscous Drag

Drift Velocity related to electric field by:

Acceleration due to electric field countered by deceleration due to scattering:

Need mobility, k, as a function of drift velocityAt low energies (E < 10 eV) data exists, for higher energies must extrapolate either using tabulated values for (n,6,4) potentials or MC simulation

kEVd

,m

eEaE

k

V

m

e

m

eEa dd

Modeling Buffer-gas Cooling:Viscous Drag

Cesium in helium extrapolation by MC method

2000 4000 6000 8000 10000 12000 14000Vd ms

50

100

150

200

250

km2 s1 V

1

Cesium in nitrogenextrapolation using tabulated values

Using this model we can calculate range and cooling timesHowever, it tells us nothing of the final properties of the cooled ions as all ions are treated equally

Modeling Buffer-gas Cooling:Viscous Drag

Cesium in 2.5x10-2 mbar HeliumRange fits with length of RFQ predetermined to be 700 mmCooling times on order of 400 μs fits well with 50 ms lifetimesRange, etc., will vary depending on weight of ion of interestCan adjust range and cooling time by varying pressure of the buffer-gas, or using heavier gas

iniv

dvvke

mR

0

,)( dvv

vk

e

mt

ini

therm

v

v

c )(

Modeling Buffer-gas Cooling:Monte Carlo

Use ion-atom interaction potential to calculate scattering angle in center of mass frame:

Relate this to energy loss in lab frame:

Runs in SIMION or separately in CTest by using to recreate experimental results for the mobility of ions in the gas

2

2

1

2

2 )(12

r

dr

E

rV

r

bbrm cm

cm

)cos()(

2

)( 22

22

cmgi

gi

gi

gi

in

sc

mm

mm

mm

mm

E

E

Modeling Buffer-gas Cooling:Monte Carlo

Lithium in helium perfect agreementCesium in helium some small discrepanciesLi+-He interaction potential well known with ab-initio calculations possibleCs+-He simple (8,6,4) potential used. Much disagreement about the proper form in the literature

Modeling Buffer-gas Cooling:Monte Carlo

RFQ defined in SIMION r0 =10 mm, L = 700 mm, Vpp = 400 V

Segmented into 24 pieces with longitudinal potential previously shown Transfer of beam with 98% efficiency

Cooling time approx. 2 x longer than that from drag model

Modeling Buffer-gas Cooling:Monte Carlo

Ions initialized in trap with T = 800 KCooled for 500 μs and then data recorded in 0.02 μs intervals for 10 μsPlot of temperature as a function of q shows the effects of RF-heatingSpace-charge not yet included so represents a minimum possible temperature

Test Setup

Injection Optics

Simulated 88% efficiency limited by radius of quadrupoles

Four-Way Switch

Use quadrupolar field to bend ions through 90o

Switch polarity to bend in opposite directionApply equal voltages to electrodes for un-deflected path

Four-Way SwitchMinimum value for h = 0.4 r0

V independent of r0 but dependant on h and ion energyWe took h = 0.15 r0

For ion energy = 30 keV, V =21.1 kV.Strength of electric field determines size of the steerer:

We took r0 = 17 mm, E ≈ 2.5 kV/mm

20

22

r

yxV

0max

2

r

VE

Extraction Optics

Extraction Methods

In absence of buffer-gas expect all bunches to have the same longitudinal and transverse emittancesFirst extraction method releases ions with a small energy spread and large time of flight spreadSecond method reduces time of flight spread but increases energy spread

Simulated Beam Properties

Buffer-gas heats beam so emittances not constantKicking the ions hard out of the trap reduces time of flight spread and increases energy spreadεrms = 3 mm mrad @ 2.5 kV

2224 xxxxrms . .

Experimental Setup

Experimental Setup

Experimental Setup: Injection

Experimental Setup: Injection

Beam through four-way switch with approx. 75% efficiencyBeam into RFQ with approx. 25% efficiencyCurrently trying to diagnose source of losesBeam charging isolators in switch?

Experimental Setup: RFQ

Experimental Setup: RFQ

Installed and Square-Wave successfully applied to the rodsBeam passed through RFQ and detected at the RFQ exit

Experimental Setup: Extraction

Experimental Setup: Extraction

Extraction optics installedMOSFET switch developed at McGill used to switch RFQ dc biasBelhke 60 kV switch used to pulse drift tubeTesting of drift tube pulser underway

Summary and OutlookDetailed simulations of cooling process in a square-wave driven RFQ carried outBased on simulations system designed and builtSquare-wave driver capable of driving large capacitive loads at high voltage and high frequency developed and testedTesting of the system underway. Emittance rig is being built so as to compare the actual beam properties to simulationTITAN platform now installed in proton hallRFQ will be installed ready for the delivery of the EBIT at the end of the summer

ThanksJens Dilling, Joe Vaz, Laura Blomeley and the rest

of the TITAN group.

Co-op Students: Robert Cussons, Ori Hadary, Amar Kamdar, George Yuan.

Triumf Support: M. Good, H. Sprenger, M. McDonald, R. Dube, R. Baartman, Controls Group,

Design Office, KICKER Group, Machine Shop, Vacuum Group.