ATOMIC ENERGY ^SLK L'ENERGIEATOMIQUE OF CANADA … · L'ENERGIE ATOMIQUE DU CANADA, LIMITEE Etude conceptuelle des plans pour la proposition d'un post-accélérateur ISOL à TRIUMF*

AECL-8960(TRI-DN-85-33)

ATOMIC ENERGY ^ S L K L'ENERGIEATOMIQUE

OF CANADA LIMITED V ^ & j F DU CANADA LIMITEE

CONCEPTUAL DESIGN STUDY FOR THE PROPOSED ISOLPOST-ACCELERATOR AT TRIUMF

Etude conceptuelle des plans pour la propositiond'un post-accelerateur ISOL a TRIUMF

G.E. McMICHAEL, B.G. CHIDLEY and R.M. HUTCHEON

Chalk River Nuclear Laboratories Laboratoires nucleates de Chalk River

Chalk River, Ontario

November 1985 novembre

ATOMIC ENERGY OF CANADA LIMITED

CONCEPTUAL DESIGN STUDY FOR THE PROPOSED ISOL POST-ACCELERATOR AT TRIUMF

by

G.E. McMichael, B.G. Chidley and R.M. Hutcheon

Accelerator Physics BranchChalk River Nuclear LaboratoriesChalk River, Ontario KOJ 1JO

1985 November

AECL-8960TRI-DN-85-33

L'ENERGIE ATOMIQUE DU CANADA, LIMITEE

Etude conceptuelle des plans pour la propositiond'un post-accélérateur ISOL à TRIUMF*

par

G.E. McMichael, B.G. Chidley et R.M. Hutcheon

Résumé

La capacité d'accélérer et d'extraire des ions lourds radioactifs pourdiverses expériences astrophysiques sera incluse dans l'installationproposée, TRIUMF ISOL. Ce rapport présente une étude conceptuelle d'unpost-accélérateur de ce genre, ayant les paramètres spécifiques del'installation TRIUMF. Ce post-accélérateur comprend un accélérateurlinéaire à 4-barres 23 MHz RFQ, capable d'accélérer de 1 à 60 keV/uma, desion? à charge unique ayant une masse allant jusqu'à 60 uma, ainsi qu'un23 MHz DTL, pour les ions à charge unique de masse 20 (ou d'ions à chargetriple ayant une masce de 60 ou moins), afin de compléter l'accélération àune valeur désirée dans la gamme de 0.265 à 1 MeV/uma. Deux cavités desceau rotateur à écartement unique réduisent l'écart d'énergie à 1 partiedans 10^ sur toute l'étendue énergétique.

*Ce travail a été. subventionné par TRIUMF et par LNCRsous le contrat 83652, 1985.

Département de la Physique des AccélérateursLaboratoires nucléaires de Chalk River

Chalk River, Ontario KGJ 1J01985 novembre

TRI-JN-85-33

ATOMIC ENERGY OF CANADA LIMITED

CONCEPTUAL DESIGN STUDY FOR THE PROPOSED ISOL POST-ACCELERATOR AT TRIUMF*

by

G.E. McMichaei, B.G. Chidley and R.M. Hutcheon

Abstract

The proposed TRIUMF ISOL facility will include the capability to accelerate the

extracted radioactive heavy ions for use in a wide range of astrophysics experi-

ments. This report presents a conceptual design for such a post-accelerator,

with parameters specific to the TRIUMF facility. It features a 4-rod 23 MHz RFQ

linac, able to accelerate singly charged ions with masses to 60 amu, from 1 to

60 keV/amu, and a 23 MHz DTL for singly charged mass 20 ions (or triply charged

ions of mass 60 or less) to complete the acceleration to any desired value in

the range 0.265 to 1 MeV/amu. Two single gap bucket rotator cavities reduce the

energy spread to 1 part in 103 over the whole energy range.

* This work was supported jointly by TRIUMFand CRNL under contract 83652, 1985.

Accelerator Physics BranchChalk River Nuclear LaboratoriesChalk River, Ontario KOJ 1J0

1985 November

AECL-8%0TRI-DN-85-33

INTRODUCTION

Specifications

The proposed TRIUMF ISOL facility will consist of a high-yield on-line isotope

separator (ISOL) and a post-accelerator with variable output energy. A con-

ceptual design for a suitable post-accelerator has been developed and was

described at a workshop on accelerated radioactive beams in September 19851.

The design study work was done at CRNL, jointly funded by TRIUMF and CRNL. This

report gives a detailed description of the results of that study.

There is considerable interest in measuring the (p,y) cross sections of radio-

active heavy nuclides in the energy range up to 1 MeV2. For nuclides with long

half-lives it is possible to build up a target of the separated isotope and

measure the cross section off-line, but for nuclides with short half lives it is

more convenient to use a beam of radioactive ions with an energy of 1.0 to

1.5 MeV/amu striking a stationary hydrogen target. The characteristics of the

accelerator are not completely settled and there is still some room for negoti-

ation between what the user would like and what he will accept on the one hand,

and what the accelerator can easily provide and what is very difficult or

expensive on the other hand. At the time this work was done the requirement was

to accelerate ions with masses up to 60 amu from an energy of 1 keV/amu to an

output energy continuously variable from 0.2 to 1.0 MeV/amu. Beam current is

low enough that space charge effects can be neglected. There is no specifi-

cation on the charge state of the ions at output, and pulse or rf structure is

not significant.

The ion beam current is limited by the production rate of the nuclide by the

TRIUMF beam. This poses restrictions on source design and pulsing capabilities,

but for design purposes it is assumed the ion source gives < 10 1 2 particles per

second of singly charged ions at 1 keV/amu (independent of mass) with a normal-

ized emittance of 0.5 TT mm mrad.

The ion beam is easier to transport and accelerate if the ions are multiply

charged and normally an ion accelerator will incorporate one or more stripper

foils to change the charge state during acceleration. After passing through a

foil thick enouqh to reach equilibrium, the beam will emerge with a distribution

of charge states. For example, at 60 keV/amu using a gas stripper the most

abundant charge state is 3. The charge number of the most abundant charge state

increases with energy so an accelerator often has several stripping foils to

keep the charge state as high as possible as the energy increases. Each

stripper involves a loss of intensity because when the most abundant charge

state is selected, the adjacent states, which are also populated, are dis-

carded. The ions in ISOL are in limited supply so stripping must be employed

with caution, and because it is most efficient, an ion source which produces

singly charged ions is preferred.

The mass range up to A = 20 amu will probably be used exclusively for the first

few years of operation and it will later be extended to A = 60. To do this the

low energy portion of the accelerator (up to 60 keV/amu) must be built witf. the

capability to accelerate singly charged ions up to 60 amu. If the remainder of

ti.e accelerator is built with the capability of accelerating singly charged ions

up to A = 20, then it can subsequently be operated with doubly charged ions up

to A = 40 and triply charged ions up to A = 60 using an appropriate stripper.

Note that up to A = 20 no stripper is used and maximum intensity is obtained.

Additional strippers or a single stripper placed at a different point are

alternatives which could be investigated more thoroughly but they appear

unlikely to provide a significant improvement.

The rf frequency of the post-accelerator is not restricted by input or output

requirements and so the choice can be made to optimize the accelerator. In

qeneral the effect of reducing frequency is to make rf structures larger and

increase the input acceptance and current limit. Because the input velocity of

the ions is low comoared to a proton accelerator and the ion source emittance is

relatively high, a low frequency is favoured. The optimum frequency of an RFQ

to cover the range 1 keV/amu to 60 keV/amu is not well defined and any value

between 10 and 50 MHz could be used.

Summary of the Proposed System

The system studied here is a two stage accelerator consisting of:

- A 4-rod RFQ to accelerate singly charged ions of mass up to 60 amu from

1 keV/amu to 60 keV/amu.

- A stripper to convert the ions between 20 and 40 amu to a charge state 2, and

ions between 40 and 60 amu to a charge state 3.

- A RILAC-type drift tube linac to accelerate either singly charged ions of mass

up to 20 amu or triply charged ions of mass 20 to 60 amu from 60 keV/amu input

energy to an output energy continuously variable from 0.2 to 1.0 MeV/amu.

- A debuncher to reduce the total output energy spread to less than 0.1%.

A frequency of 23 MHz was chosen because it was the same as the TRIUMF rf

system, so equipment and expertise should be readily available, and because

acceptance and size were both suitable.

The RFQ is designed to accept an input beam of:

Mass 60 amu

Charge 1

Energy 1 keV'amu U = 0.0015)

Current < 1 yA

Normalized Emittance Invariant 0.5 v mm mrad

The beam line from the RFQ to the drift tube linac should have a total length

less than 80 cm to prevent debunching and the minimum distance from the end of

the vane to the start of the first quadrupole 10 cm. A beam with the same

emittance ellipse parameters as at the exit of the RFQ is acceptable to the DTL

so a null transformation will be sought for this beam transport line. The beam

at the stripper should be as small as possible to minimize effects of multiple

scattering and in the case of a gas stripper reduce the problems associated with

differential pumping.

BEAM DYNAMICS

RFQ

The particle dynamics is insensitive to the fields beyond the region at the vane

tips which contain the beam, so the computer programs PARMTEQ, CURLI and RFQUIK,

which were written for a 4-vane RFQ, are equally applicable to a 4-rod design.

PARMTEQ was written originally for protons as the accelerated ions. Options to

handle ions with a different mass and charge state were included, but the code

would not allow the ion mass or charge state to be varied between the design and

particle tracing phases. Modifications to the code to permit such calculations

have been installed.

An RFQ will accelerate particles only if their velocity at each cell matches the

design velocity, i.e., the ions must have the correct energy per nucleon. If

ions with a charge to mass ratio different from the design value are to be

accelerated, the vane voltage must be changed. For example, an RFQ designed for

ions of mass 60 amu will accelerate ions of mass 30 with the same velocity if

the RFQ vane voltage is reduced by a factor of two. Note that for reasons of

efficiency an RFQ is usually designed with the vane voltage close to the

sparking limit. It therefore can be operated below the design voltage, but not

above. This means the RFQ should be designed for the ion of smallest charge to

mass ratio which it will be required to accelerate and then lighter ions or ions

of a higher charge state can be accelerated by reducing the rf excitation power.

A 4-vane RFQ is normally designed with a constant mean beam aperture because

this gives a constant capacitance per unit length and hence a uniform excitation

with a structure of constant outside diameter. In a 4-rod RFQ it is relatively

easy to vary the inductance along the length to compensate for a change in mean

aperture and to tilt the rf fields from end to end. Increasing the aperture and

vane voltage with ion velocity can lead to a reduction of accelerator total

length. The detailed parameters of the RFQ are listed in Table 1. It operates

at 23 MHz and has a peak electric field of 1.5 times the Kilpatrick criterion3.

The RFQ has a total vane length of 919.7 cm and has a tapered bore with constant

e lec t r i c f i e l d strength. A similar design with a constant bore is shown in

Table 2 and has a total vane length of 1505 cm; the length reduction is gained

by the tapered bore design.

The output energy was chosen to be 3.6 MeV (60 keV/amu) to give e f f i c i en t

str ipping of mass 60 ions to charge state 3. Transmission is 86% for a normal-

ized emittance invariant at input of 0.46 ir mm mrad.

The input e l l ipse parameters are: ax = -1.507

tix = 0.781 mrn/mrad

ay = +1.507

iiy = 0.781 mm/mrad

Stripper

In principle either a gas stripper or a carbon foil could be used to convert the

ions i,o a charge state 3. The average equilibrium charge state for a 3.6 MeV

ion of mass 60 is around 3 for a gas stripper and 5 for a carbon foil. In

either case a thickness of 0.3 ygm/cm2 is adequate (a thicker stripper could be

used but would give higher multiple scattering). A gas stripper of this

thickness is feasible, but minimum foils are an order of magnitude thicker.

Small angle multiple scattering of nickel ions has been calculated4 for a

5 ngm/cm2 carbon foil bombarded by 3.6 MeV nickel ions (mass = 59), Lindhard's5

reduced energy parameter e is 33.3 and the reduced thickness parameter

T is 1.38. Using Sigmund and Winterbon6 and taking the 2a point in the

scattering distribution we obtain ^_a - 4.2 mrad. This must be added in

quadrature with the "emittance divergence" of the beam to get the divergence of

the beam after stripping.

For a gas stripper, 0.3 pgrn/cm2 thickness of nitroqen would have e = 31.9 and

T = 0.069 giving a ^Za of 0.34 mrad. Even if the analysis is not accurate for

so thin a target, it aopears that the emittance growth from gas stripping can be

ignored.

Table 1

RFQ Parameters

22 30 .40 ,FREQ= 23.00 MHZ, Q=1.0,WI= .060,WF= 3.60 AMU=60.00 1= O.OMA

TANK 1 LENGTH= 919.72 CM, 318 CELLS

NC012345678910111213141516171819202122232425262728293031323334353637383940414243

V.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038

US.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.060.061.061.061.061.061.061.061.061.061.061.061.062.062.062.062.062

BETA.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015.0015

000000

<

<

EZ.000.000.000.000.000.000.003.005.008.011.013.016.019.021.024.026.029.032.034.037.040.042.045.047.050.053.055.058.060.063.065.068.070.072.075.077.080.082.085,087,090,092,095,097

000000

CAPA.000.000.000.000.000.000.001.001.002.003.003.004.005.005.006.007.007.008.009.009.010.011.011.012.013.013.014.015.015.016.016.017.018.018.019.020,020,021,022.022,023024024025

PHI-90-90-90-90-90-90-89-89-89-88.-88-88.-87.-87-87-86,-86.-86.-85.-85.-85.-84.-84.-84.-84.-83.-83.-83.-82.-82.-82.-81.-81.-81.-80.-80.-80.-79.-79.-79.-78.-78.-78.-77.

.0

.0

.0

.0

.0

.0

.7

.4

.1

.7

.4

.1

.8

.5

.2

.8

.5

.2

.9

.6

.3,9,63.0,7,4.0.7418518529529639

A2.2311.019.761.634.555.499.499.499.498.498.498.497.497.497.497.496.496.496.495.495.495.494.494.494.494.493.493.493.493.492.492.492.491.491.491.491.490.490.490.489.489.489.489.488

1111111-1X

111111111111.11111,1.1.1.1,1,1,1.1.1.1.1.1.1.1.1.1.1.1.1.

M.000.000.000.000.000.000.001.002.004.005.006.007.008.010.011.012.013.014.016.017.018.019.020.022.023.024.025.026.027.029.030.031,032033034036037038039040041043044045

112344444444444444444444444444.44,4.4,4.4.4.4.4.4.4.4.4.

B.23.11.99.87.75.63.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64,64.64,6464646464

000000—_____________-__

_______,-,_,_,_,-,_,_,_,

-.—,_,

RFD.00.00.00.00.00.00.00.00.00.00.01.01.01.01.01.01.01.01.01.01.02.02.02.02.02.02.02.02.02.02.03.03.03.03.03.03,03,03,03.0303040404

CL

.95

.95

.95

.95

.95

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.96

.97

.97

.97

.97

.97

.9?

.97

TL

123456789101112131415161718,1920,21.22,22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.41.

.95

.91

.86

.82

.77

.73

.69

.64

.60

.56

.51

.47

.43

.39

.34

.30

.26

.21

.17

.13

.09

.04

.00

.96

.92

.88

.84,8076,7268646157535046434037333 i

?n

Table 1 (cont'd)NC V US BETA EZ CAPA PHI AM B RFD CL TL44 .038 .062 .0015 .100 .026 -77.6 .488 1.046 4.64 -.04 .97 42.2545 .038 .062 .0015 .102 .026 -77.3 .488 1.047 4.64 -.04 .97 43.2246 .038 .063 .0015 .105 .027 -77.0 .488 1.048 4.64 -.04 .98 44.2047 .038 .063 .0015 .107 .028 -76.7 .487 1.050 4.64 -.04 .98 45.1848 .038 .063 .0015 .110 .028 -76.3 .487 1.051 4.64 -.04 .98 46.1649 .038 .063 .0015 .112 .029 -76.0 .487 1.052 4.64 -.04 .98 47.1450 .038 .063 .0015 .115 .030 -75.7 .486 1.053 4.64 -.04 .98 48.1251 .038 .064 .0015 .117 .030 -75.4 .486 1.054 4.64 -.04 .98 49.1052 .038 .064 .0015 .120 .031 -75.0 .486 1.056 4.64 -.04 .99 50.0953 .038 .064 .0015 .122 .032 -74.7 .486 1.057 4.64 -.04 .99 51.0754 .038 .064 .0015 .125 .032 -74.4 .485 1.058 4.64 -.05 .99 52.0655 .038 .065 .0015 .127 .033 -74.1 .485 1.059 4.64 -.05 .99 53.0556 .038 .065 .0015 .130 .034 -73.7 .485 1.060 4.64 -.05 .99 54.0557 .038 .065 .0015 .132 .035 -73.4 .485 1.061 4.64 -.05 1.00 55.0458 .038 .066 .0015 .135 .035 -73.1 .484 1.063 4.64 -.05 1.00 56.0459 .038 .066 .0015 .137 .036 -72.7 .484 1.064 4.64 -.05 1.00 57.0460 .038 .066 .0015 .139 .037 -72.4 .484 1.065 4.64 -.05 1.00 58.0461 .038 .067 .0015 .142 .038 -72.1 .483 1.066 4.64 -.05 1.00 59.0562 .038 .067 .0015 .144 .038 -71.7 .483 1.067 4.64 -.05 1.01 60.0563 .038 .067 .0016 .146 .039 -71.4 .483 1.068 4.64 -.05 1.01 61.0664 .038 .068 .0016 .148 .040 -71.1 .483 1.069 4.64 -.05 1.01 62.0865 .038 .068 .0016 .150 .040 -70.7 .482 1.070 4.64 -.05 1.02 63.0966 .038 .068 .0016 .152 .041 -70.4 .482 1.071 4.64 -.05 1.02 64.1167 .038 .069 .0016 .154 .042 -70.1 .482 1.072 4.64 -.05 1.02 65.1368 .038 .069 .0016 .157 .042 -69.7 .482 1.073 4.64 -.05 1.03 66.1669 .038 .070 .0016 .159 .043 -69.4 .482 1.074 4.64 -.05 1.03 67.1970 .038 .070 .0016 .161 .044 -69.0 .481 1.075 4.64 -.05 1.03 68.2271 .038 .071 .0016 .163 .044 -68.7 .481 1.076 4.64 -.05 1.04 69.2572 .038 .071 .0016 .165 .045 -68.4 .481 1.077 4.64 -.06 1.04 70.2973 .038 .072 .0016 .167 .046 -68.0 .481 1.079 4.64 -.06 1.04 71.3374 .038 .072 .0016 .169 .046 -67.7 .480 1.080 4.64 -.06 1.05 72.3875 .038 .073 .0016 .171 .047 -67.3 .480 1.081 4.64 -.06 1.05 73.4376 .038 .073 .0016 .173 .048 -67.0 .480 1.082 4.64 -.06 1.05 74.4877 .038 .074 .0016 .175 .049 -66.6 .480 1.083 4.64 -.06 1.06 75.5478 .038 .074 .0016 .177 .049 -66.3 .479 1.084 4.64 -.06 1.06 76.6079 .038 .075 .0016 .179 .050 -65.9 .479 1.085 4.64 -.06 1.07 77.6780 .038 .076 .0016 .181 .051 -65.6 .479 1.086 4.64 -.06 1.07 78.7481 .038 .076 .0017 .182 .051 -65.4 .479 1.086 4.64 -.06 1.07 79.8282 .038 .077 .0017 .183 .052 -65.2 .479 1.087 4.64 -.06 1.08 80.9083 .038 .078 .0017 .185 .053 -64.9 .478 1.088 4.64 -.06 1.08 81.9884 .038 .078 .0017 .186 .053 -64.7 .478 1.089 4.64 -.06 1.09 83.0785 .038 .079 .0017 .188 .054 -64.4 .478 1.089 4.64 -.06 1.09 84.1686 .038 .080 .0017 .189 .055 -64.1 .478 1.090 4.64 -.06 1.10 85.2687 .038 .080 .0017 .191 .055 -63.9 .478 1.091 4.64 -.06 1.10 86.3688 .038 .081 .0017 .192 .056 -63.6 .478 1.092 4.64 -.06 1.11 87.4789 .038 .082 .0017 .194 .057 -63.4 .477 1.093 4.64 -.06 1.11 88.5890 .038 .083 .0017 .195 .057 -63.1 .477 1.093 4.64 -.06 1.12 89.7091 .038 .084 .0017 .196 .058 -62.9 .477 1.094 4.64 -.06 1.12 90.8392 .038 .084 .0017 .198 .059 -62.6 .477 1.095 4.64 -.06 1.13 91.9693 .038 .085 .0017 .199 .059 -62.4 .477 1.096 4.64 -.06 1.13 93.0994 .038 .086 .0018 .201 .060 -62.1 .476 1.097 4.64 -.06 1.14 94.2395 .038 .087 .0018 .202 .061 -61.8 .476 1.098 4.64 -.06 1.15 95.3896 .038 .088 .0018 .203 .062 -61.6 .476 1.098 4.64 -.06 1.15 96.5397 .038 .089 .0018 .205 .062 -61.3 .476 1.099 4.64 -.06 1.16 97.6998 .038 .090 .0018 .206 .063 -61.0 .476 1.100 4.64 -.06 1.16 98.85

Table 1 (cont'd)NC99100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153

V.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038

ws.090.091.092.093.094.095.096.097.099.100.101.102.103.104.106.107.108.110.111.112.114.115.117.119.120.122.123.125.127.129.131.133.135.137.139.141.143.145.148.150.153.155.158.161.164.166.169.173.176.179.182.186.190.193.197

BETA.0018.0018.0018.0018.0018.0018.0019.0019.0019.0019.0019.0019.0019.0019.0019.0020.0020.0020.0020.0020.0020.0020.0020.0021.0021.0021.0021.0021.0021.0021.0022.0022.0022.0022.0022.0022.0023.0023.0023.0023.0023.0024.0024.0024.0024.0024.0025.0025.0025.0025.0026.0026.0026.0026.0027

EZ.208.209.210.212.213.214.216.217.218.221.223.226.228.230.233.235.238.240.243.245.247.250.252.254.257.259.262.266.270.273.277.280.284.288.291.295.298.301.306.311.316.320.325.329.334.338.343.349.355.361.367.373.379.385.393

CAPA.064.065.065.066.067.068.069.069.070.071.072.074.075.076.077.079.080.081.083.084.085.087.088.090.091.092.094.096.098.100.102.104.107.109.111.113.115.118.120.123.126.129.132.135.138.141.144.148.152.156.160.164.169.173.178

PHI-60-60-60-59-59-59-59-58-58-58-58-57-57-57-56-56-56-55.-55-55-54-54-54,-53,-53,-53.-52,-52,-52,-51.-51.-51.-50.-50.-50.-49.-49.-49.-48.-48.-47.-47.-47.-46.-46.-46.-45.-45.-44.-44.-44.-43.-43.-42.-42.

.8

.5

.2

.9

.7

.4

.1

.8

.6

.3

.0

.7

.4

.0

.7

.4

.1

.8

.5

.2

.8

.5

.2

.9

.5

.2

.9

.5

.2

.8

.5

.1,8,4.1.7.4.0,63951740628406284

A.476.475.475.475.475.475.474.474.474.474.473.473.473.472.472.472.471.471.470.470.470.469.469.469.468.468.467.467.466.466.465.465.464.463.463.462.462.461.460.459.459.458.457.456.455.455.454.453.451.450.449.448.447.446.444

M1.1011.1021.1031.1031.1041.1051.1061.1071.1081.1091.1111.1121.1141.1151.1171.1181.1201.1221.1231.1251.1261.1281.1301.1311.1331.1351.1371.1391.1421.1441.1471.1501.1521.1551.1581.1601.1631.1661.1691.1731.1771.1801.1841.1881.1921.1961.2001.2051.2101.2161.2211.2261.2321.2381.245

4444444444444444444444444444444444444444,4,4,4.4.4.4.4.4.4.4.4.4.4.4.4.

B.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.64.63.63.63.63.63.63.63,63.63.63.63.63.63.63.63.63.6363

RFD-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06

1111111111111111111111111111111,111.11,1,1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.1.

CL.17.18.18.19.19.20.21.21.22.23.23.24.25.26.26.27.28.29.30.30.31.32.33.34.35.36.37.38.38.39.40.42.43.44.45.46.47.48.49,51.52,53,54565758606163646667697172

TL100101102103104105107108109110112113114115117118119120122123124126127128130131132134135137138.139,141,142.144,145.147,148.150.151.153.154.156.157.159.160.162.164.165.167.169.170.172.174.175.

.02

.19

.38

.56

.76

.96

.17

.38

.60

.83

.06

.31

.55

.81

.07

.35

.63

.91

.21

.51

.82

.14

.47

.81

.16

.52

.88

.26

.64

.04

.44

.86

.28

.72

.17

.63

.10

.58,07,58.106317733088481072370370391082

Table 1 (con t 'd )

NC154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208

V.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.039.039.040.040.041.041.042.042.043.043.044.044.045.046.046.047.047.048.049.049.050.050.051.052.052.053

WS.201.205-210.214.219.224.229.234.239.245.251.257.263.269.276.283.291.299.307.315.324.333.343.353.364.375.386.399.412.425.438.451.464.478.492.506.520.534.549.564.578.594.609.624.640.656.672.688.705.721.738.755.773.790.808

BETA.0027.0027.0027.0028.0028.0028.0029.0029.0029.0030.0030.0030.0031.0031.0031.0032.0032.0033.0033.0034.0034.0035.0035.0036.0036.0037.0037.0038.0038.0039.0040.0040.0041.0041.0042.0043.0043.0044.0044.0045.0045.0046.0047.0047.0048.0048.0049.0050.0050.0051.0051.0052.0053.0053.0054

EZ.401.408.416.423.431.440.449.458.466.477.488.498.509.521.534.546.560.574.588.605.622.639.655.670.689.709.731.753.772.758.755.753.752.751.750.749.748.747.747.746.746.746.746.746.746.746.746.747.747.748.748.749.749.750.751

CAPA.184.189.194.200.206.213.219.226.233.241.249.258.266.276.286.296.308.320.332.346.361.376.391.406.424.442.463.484.505.491.491.492.492.492.492.493.493.493.493.494.494.494.494.494.494.494.494.494.494.494.494.494.494.494.494

PHI-42-41-41-40-40-39-39-39-38-38-37-37-36-36-36-35-35-34-34-33-33-32-32.-32-31.-31-30.-30-29.-30,-30.-30,-30,-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.-30.

.0

.6

.2

.8

.3

.9

.5

.1

.6

.2

.8

.4

.9

.5

.0

.6

.2

.7

.3

.8

.4

.9

.5

.0

.5

.1

.6

.1

.7

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.00000000000000

A.443.441.440.438.436.434.432.430.429.426.424.421.419.416.413.410.406.403.399.395.390.385.381.376.370.364.357.350.343.354.357.361.364.368.372.376.380.384.388.392.397.401.406.410.415.420.425.430.435.441.446.452.458.464.470

111111111111111111111111111111111111111111111111111.1.1.1.1.

M.252.260.267.275.283.293.302.312.321.334.346.359.372.387.403.419.438.458.478.503.531.558.586.615.651.690.736.785.836.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800.800

44444444444444444444444444444444444444444444333333,3,3.3.3.3.

B.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.63.58.54.50.47.43.39.36.32.28.24.20.16.12.07.03.99.95.90.86.81.77.72.67.63.58,53

RFD-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06.06

- 06-.06-.06-.06-.06-.06-.06-.06-.06-.05-.05-.05-.05-.05-.05-.05-.05-.05-.05-.05-.05-.05-.05-.04-.04-.04-.04-.04-.04-.04-.04-.04-.04

11111111111112222222222222.222222222222222233333333,3.3,3,3,3.

CL.74.76.78.80.82.84.86.88.90.92.94.97.99.01.04.06.09.12.15.18.21.24.27.30.34.37.41.45.48.51.56.59.63.67.71.75.79.83.87.90.94.98.02.06.10.13.17.21.25.29.33.37.40.44.48

TL177.56179.32181.10182.90184.71186.55188.40190.28192.18194.10196.04198.00199.99202.01204.04206.11208.20210.32212.46214.64216.85219.08221.35223.65225.99228.36230.77233,21235.70238.21240.76243.36245.99248.67251.38254.13256.92259.74262.61265.51268.45271.43274.45277.51280.61283.74286.91290.13293.38296.66299.99303.36306.76310.20313.68

10

Table 1 (cont'd)NC V WS BETA EZ CAPA PHI A M B RFD CL TL209 .054 .826 .0054 .751 .493 -30.0 .476 1.800 3.48 -.04 3.52 317.20210 .054 .844 .0055 .752 .493 -30.0 .482 1.800 3.43 -.04 3.56 320.76211 .055 .862 .0056 .75.3 .493 -30.0 .489 1.800 3.38 -.04 3.60 324.36212 .056 .881 .0056 .754 .493 -30.0 .496 1.800 3.33 -.04 3.64 328.00213 .056 .900 .0057 .755 .493 -30.0 .503 1.800 3.28 -.04 3.68 331.67214 .057 .919 .0057 .756 .492 -30.0 .510 1.800 3.23 -.04 3.71 335.39215 .058 .938 .0058 .757 .492 -30.0 .517 1.800 3.18 -.04 3.75 339.14216 .058 .958 .0059 .758 .492 -30.0 .525 1.800 3.13 -.04 3.79 342.93217 .059 .977 .0059 .759 .492 -30.0 .533 1.800 3.07 -.04 3.83 346.76218 .060 .997 .0060 .760 .491 -30.0 .541 1.800 3.02 -.04 3.87 350.63219 .061 1.018 .0060 .761 .491 -30.0 .549 1.800 2.96 -.04 3.91 354.54220 .061 1.038 .0061 .760 .491 -30.0 .554 1.800 2.93 -.04 3.95 358.49221 .061 1.058 .0062 .756 .491 -30.0 .556 1.800 2.92 -.04 3.99 362.48222 .062 1.079 .0062 .753 .492 -30.0 .558 1.800 2.92 -.04 4.03 366.50223 .062 1.100 .0063 .749 .492 -30.0 .560 1.800 2.91 -.03 4.07 370.57224 .062 1.121 .0063 .746 .493 -30.0 .562 1.800 2.90 -.03 4.10 374.67225 .062 1.142 .0064 .743 .493 -30.0 .563 1.800 2.89 -.03 4.14 378.82226 .063 1.163 .0065 .740 .493 -30.0 .565 1.800 2.88 -.03 4.18 383.00227 .063 1.184 .0065 .737 .494 -30.0 .567 1.800 2.88 -.03 4.22 387.22228 .063 1.205 ,0066 .734 .494 -30.0 .569 1.800 2.87 -.03 4.26 391.47229 .063 1.226 .0066 .731 .495 -30.0 .571 1.800 2.86 -.03 4.29 395.77230 .064 1.248 .0067 .728 .495 -30.0 .573 1.800 2.85 -.03 4.33 400.10231 .064 1.269 .0067 .726 .495 -30.0 .575 1.800 2.84 -.03 4.37 404.47232 .064 1.291 .0068 .723 .496 -30.0 .577 1.800 2.83 -.03 4.41 408.88233 .065 1.313 .0069 .721 .496 -30.0 .579 1.800 2.83 -.03 4.44 413.32234 .065 1.335 .0069 .718 .496 -30.0 .581 1.800 2.82 -.03 4.48 417.81235 .065 1.357 .0070 .716 .496 -30.0 .584 1.800 2.81 -.03 4.52 422.32236 .065 1.379 .0070 .713 .497 -30.0 .586 1.800 2.80 -.03 4.56 426.88237 .066 1.401 .0071 .711 .497 -30.0 .588 1.800 2.79 -.03 4.59 431.47238 .066 1.423 .0071 .709 .497 -30.0 .590 1.800 2.78 -.03 4.63 436.10239 .066 1.446 .0072 .707 .497 -30.0 .592 1.800 2.77 -.03 4.67 440.77240 .067 1.468 .0072 .705 .498 -30.0 .595 1 8 0 0 2.76 -.03 4.70 445.47241 .067 1.491 .0073 .703 .498 -30.0 .597 1.800 2.76 -.03 4.74 450.21242 .067 1.514 .0074 .701 .498 -30.0 .599 1.800 2.75 -.03 4.78 454.99243 .068 1.537 .0074 .699 .498 -30.0 .601 1.800 2.74 -.03 4.81 459.80244 .068 1.560 .0075 .698 .499 -30.0 .604 1.800 2.73 -.03 4.85 464.64245 .068 1.583 .0075 .696 .499 -30.0 .606 1.800 2.72 -.03 4.88 469.53246 .068 1.606 .0076 .694 .499 -30.0 .609 1.800 2.71 -.03 4.92 474.45247 .069 1.629 .0076 .693 .499 -30.0 .611 1.800 2.70 -.03 4.96 479.40248 .069 1.653 .0077 .691 .499 -30.0 .613 1.800 2.69 -.03 4.99 484.39249 .069 1.676 .0077 .690 .499 -30.0 .616 1.800 2.68 -.03 5.03 489.42250 .070 1.700 .0078 .688 .500 -30.0 .618 1.800 2.67 -.03 5.06 494.48251 .070 1.724 .0079 .687 .500 -30.0 .621 1.800 2.66 -.03 5.10 499.58252 .070 1.748 .0079 .685 .500 -30.0 .623 1.800 2.65 -.03 5.13 504.71253 .071 1.772 .0080 .684 .500 -30.0 .626 1.800 2.64 -.02 5.17 509.88254 .071 1.796 .0080 .683 .500 -30.0 .629 1.800 2.63 -.02 5.20 515.08255 .071 1.820 .0081 .682 .500 -30.0 .631 1.800 2.62 -.02 5.24 520.32256 .072 1.845 .0081 .680 .501 -30.0 .634 1.800 2.61 -.02 5.27 525.60257 .072 1.869 .0082 .679 .501 -30.0 .637 1.800 2.60 -.02 5.31 530.91258 .072 1.894 .0082 .678 .501 -30.0 .639 1.800 2.59 -.02 5.34 536.25259 .073 1.919 .0083 .677 .501 -30.0 .642 1.800 2.58 -.02 5.38 541.63260 .073 1.944 .0083 .676 .501 -30.0 .645 1.800 2.57 -.02 5.41 547.05261 .073 1.969 .0084 .675 .501 -30.0 .648 1.800 2.56 -.02 5.45 552.49262 .074 1.994 .0084 .674 .501 -30.0 .651 1.800 2.55 -.02 5.48 557.98263 .074 2.019 .0085 .673 .501 -30.0 .653 1.800 2.54 -.02 5.52 563.50

11

Table 1 (cont'd)NC V WS BETA EZ CAPA PHI AM B RFD CL TL264 .074 2.044 .0086 .672 .501 -30.0 ,656 1.800 2.53 -.02 5.55 569.05265 .075 2.070 .0086 .671 .501 -30.0 .659 1.800 2.52 -.02 5.59 574.64266 .075 2.095 .0087 .671 .502 -30.0 .662 1.800 2.51 -.02 5.62 580.26267 .076 2.121 .0087 .670 .502 -30.0 .665 1.800 2.50 -.02 5.66 585.92268 .076 2.147 .0088 .669 .502 -30.0 .668 1.800 2.48 -.02 5.69 591.61269 .076 2.173 .0088 .668 .502 -30.0 .671 1.800 2.47 -.02 5.73 597.34270 .077 2.199 .0089 .667 .502 -30.0 .674 1.800 2.46 -.02 5.76 603.10271 .077 2.226 .0089 .667 .502 -30.0 .678 1.800 2.45 -.02 5.80 608.89272 .077 2.252 .0090 .666 .502 -30.0 .681 1.800 2.44 -.02 5.83 614.72273 .078 2.278 .0090 .665 .502 -30.0 .684 1.800 2.43 -.02 5.86 620.59274 .078 2.305 .0091 .665 .502 -30.0 .687 1.800 2.42 -.02 5.90 626.49275 .078 2.332 .0091 .664 .502 -30.0 .690 1.800 2.41 -.02 5.93 632.42276 .079 2.359 .0092 .664 .502 -30.0 .694 1.800 2.39 -.02 5.97 638.39277 .079 2.386 .0092 .663 .502 -30.0 .697 1.800 2.38 -.02 6.00 644.39278 .080 2.413 .0093 .663 .502 -30.0 .700 1.800 2.37 -.02 6.04 650.42279 .080 2.440 .0093 .662 .502 -30.0 .704 1.800 2.36 -.02 6.07 656.49280 .080 2.468 .0094 .662 .502 -30.0 .707 1.800 2.35 -.02 6.10 662.60281 .081 2.495 .0094 .661 .502 -30.0 .711 1.800 2.34 -.02 6.14 668.74282 .081 2.523 .0095 .661 .502 -30.0 .714 1.800 2.32 -.02 6.17 674.91283 .082 2.551 .0096 .660 .503 -30.0 .718 1.800 2.31 -.02 6.21 681.11284 .082 2.579 .0096 .660 .503 -30.0 .721 1.800 2.30 -.02 6.24 687.36285 .082 2.607 .0097 .660 .503 -30.0 .725 1.800 2.29 -.02 6.27 693.63286 .083 2.635 .0097 .659 .503 -30.0 .729 1.800 2.28 -.02 6.31 699.94287 .083 2.664 .0098 .659 .503 -30.0 .733 1.800 2.26 -.02 6.34 706.28288 .084 2.692 .0098 .659 .503 -30.0 .736 1.800 2.25 -.02 6.38 712.66289 .084 2.721 .00«9 .658 .503 -30.0 .740 1.800 2.24 -.02 6.41 719.07290 .084 2.750 .0099 .658 .503 -30.0 .744 1.800 2.23 -.02 6.44 725.51291 .085 2.779 .0100 .658 .503 -30.0 .748 1.800 2.22 -.02 6.48 731.99292 .085 2.808 .0100 .658 .503 -30.0 .752 1.800 2.20 -.02 6.51 738.50293 .086 2.837 .0101 .657 .503 -30.0 .756 1.800 2.19 -.02 6.55 745.05294 .086 2.867 .0101 .657 .503 -30.0 .760 1.800 2.18 -.02 6.58 751.63295 .086 2.896 .0102 .657 .503 -30.0 .764 1.800 2.17 -.02 6.61 758.24296 .087 2.926 .0102 .657 .503 -30.0 .768 1.800 2.15 -.02 6.65 764.89297 .087 2.956 .0103 .657 .503 -30.0 .772 1.800 2.14 -.02 6.68 771.58298 .088 2.986 .0103 .656 .503 -30.0 .776 1.800 2.13 -.02 6.72 778.29299 .088 3.016 .0104 .656 .503 -30.0 .781 1.800 2.11 -.02 6.75 785.04300.089 3.046.0104 .656 .502-30.0 .785 1.800 2.10 -.02 6.78 791.82301 .089 3.076 .0105 .656 .502 -30.0 .789 1.800 2.09 -.02 6.82 798.64302 .089 3.107 .0105 .656 .502 -30.0 .794 1.800 2.07 -,02 6.85 805.49303 .090 3.138 .0106 .656 .502 -30.0 .798 1.800 2.06 -.02 6.89 812.38304 .090 3.168 .0106 .656 .502 -30.0 .803 1.800 2.05 -.02 6.92 819.30305 .091 3.199 .0107 .656 .502 -30.0 .807 1.800 2.03 -.02 6.95 826.25306 .091 3.230 .0108 .656 .502 -30.0 .812 1.800 2.02 -.02 6.99 833.24307 .092 3.262 .0108 .656 .502 -30.0 .817 1.800 2.01 -.02 7.02 840.26308 .092 3.293 .0109 .656 .502 -30.0 .822 1.800 1.99 -.02 7.05 847.31309 .093 3.325 .0109 .656 .502 -30.0 .826 1.800 1.98 -.02 7.09 854.40310 .093 3.357 .0110 .656 .502 -30.0 .831 1.800 1.97 -.02 7.12 861.52311 .093 3.388 .0110 .656 .502 -30.0 .836 1.800 1.95 -.02 7.16 868.68312 .094 3.420 .0111 .656 .502 -30.0 .841 1.800 1.94 -.02 7.19 875.87313 .094 3.453 .0111 .656 .502 -30.0 .846 1.800 1.93 -.02 7.22 883.09314 .095 3.485 .0112 .656 .502 -30.0 .852 1.800 1.91 -.02 7.26 890.35315 .095 3.517 .0112 .656 .502 -30.0 .857 1.800 1.90 -.02 7.29 897.64316 .096 3.550 .0113 .656 .502 -30.0 .862 1.800 1.88 -.02 7.33 904.97317 .096 3.583 .0113 .656 .502 -30.0 .867 1.800 1.87 -.02 7.36 912.33318 .097 3.616 .0114 .656 .501 -30.0 .873 1.800 1.86 -.02 7.39 919.72

12

Table 2

RFQ Parameters Assuming Constant Vane Voltage

22 30 .40 ,FREQ= 23.00 MHZ, Q=1.0,WI= .060,WF= 3.60 AMU=60.00 1= O.OMA

TANK 1 LENGTH= 1505.31 CM, 420 CELLS

NC05101520253035404550556065707580859095100105110115120125130135140145150155160165170175180185190195

V.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038.038

ws.060.060.060.060.060.060.061.061.062.062.063.065.066.068.070.073.076.079.083.087.091.096.102.108.115.123.133.143.155.169.186.205.229.257.291.333.386.450.514.579

BETA.0015.0015.0015.0015,0015.0015.0015.0015.0015.0015.0015.0015.0015.0016.0016.0016.0016.0017.0017.0018.0018.0019.0019.0020.0020.0021.0022.0023.0024.0025.0026.0027.0029.0030.0032.0035.0037.0040.0043.0046

EZ0.0000.000.013.026.040.053.065.077.090.102.115.127.139.150.161.171.181.188.195.202.209.216.226.238.250.262.280.298.320.343.373.408.449.498.560.639.731.724.682.647

CAPA0.0000.000.003.007.010.013.016.020.023.026.030.033.037.040.044.047.051.054.057.061.065.069.074.080.087.094.104.115.129.144.164.189.219.258.308.376.463.494.498.502

PHI-90.0-90.0-88.4-86.8-85.3-83.7-82.1-80.5-78.9-77.3-75.7-74.1-72.4-70.7-69.0-67.3-65.6-64.4-63.1-61.8-60.5-59.1-57.7-56.1-54.5-52.9-51.1-49.4-47.5-45.6-43.6-41.6-39.5-37.4-35.2-32.9-30.6-30.0-30.0-30.0

A2.231.499.498.496.495.493.492.491.489.488.486.485.484.482.481.480.479.478.477.476.475.474.473.471.469.467.465.462.458.454.448.441.432.421.406.385.357.347.347.346

M1.0001.0001.0061.0121.0181.0241.0301.0361.0411.0471.0531.0591.0651.0701.0751.0811.0861.0891.0931.0981.1021.1061.1121.1201.1281.1371.1501.1631.1801.2001.2261.2601.3021.3591.4381.5581.7361.8001.8001.800

B.23

4.634.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.644.634.634.634.634.634.634.634.634.634.634.634.63

RFD0.000.00-.01-.01-.02-.02-.03-.03-.03-.04-.04-.05-.05-.05-.05-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.06-.05-.05-.04

11111111111111111111112222.2.2,

CL

.95

.96

.96

.96

.96

.96

.96

.97

.97

.98

.99

.00

.02

.03

.05

.07

.09

.12

.15

.18

.21

.24

.28

.32

.37

.42

.47

.53

.60

.67

.76

.86

.97

.09

.24

.41

.59

.78

.95

TL

4.779.5614.3419.1323.9228.7233.5338.3743.2248.1253.0558.0463.0968.2273.4378.7484.1689.7095.38101.19107.17113.31119.63126.14132.88139.86147.10154.63162.48170.70179.32188.40198.00208.20219.08230.77243.36256.87271.27

13

Table 2 (cont1d)NC V WS BETA EZ CAPA PHI M B RFD CL TL200 .038 .644 .0048205 .038 .710 .0050210 .038 .776 .0053215 .038 .842 .0055220 .038 .908 .0057225 .038 .974 .0059230 .038 1.040 .0061235 .038 1.107 .0063240 .038 1.174 .0065245 .038 1.240 .0067250 .038 1.307 .0068255 .038 1.374 .0070260 .038 1.441 .0072265 .038 1.508 .0073270 .038 1.575 .0075275 .038 1.642 .0077280 .038 1.709 .0078285 .038 1.776 .0080290 .038 1.844 .0081295 .038 1.911 .0083300 .038 1.978 .0084305 .038 2.046 .0086310 .038 2.113 .0087315 .038 2.180 .0088320 .038 2.248 .0090325 .038 2.315 .0091330 .038 2.383 .0092335 .038 2.450 .0094340 .038 2.518 .0095345 .038 2.585 .0096350 .038 2.653 .0097355 .038 2.720 .0099360 .038 2.788 .0100365 .038 2.856 .0101370 .038 2.923 .0102375 .038 2.991 .0103380 .038 3.058 .0105385 .038 3.126 .0106390 .038 3.194 .0107395 .038 3.261 .0108400 .038 3.329 .0109405 .038 3.397 .0110410 .038 3.465 .0111415 .038 3.532 .0112420 .038 3.600 .0113

.616 .504 -30.0

.589 .507 -30.0

.566 .508 -30.0

.544 .510 -30.0

.525 .511 -30.0

.508 .512 -30.0

.493 .513 -30.0

.478 .514 -30.0

.465 .515 -30.0

.453 .516 -30.0

.442 .517 -30.0

.431 .517 -30.0

.421 .518 -30.0

.412 .518 -30.0

.404 .519 -30.0

.396 .519 -30.0

.388 .519 -30.0

.381 .520 -30.0

.374 .520 -30.0

.368 .520 -30.0

.361 .521 -30.0

.356 .521 -30.0

.350 .521 -30.0

.345 .521 -30.0

.340 .521 -30.0

.335 .522 -30.0

.330 .522 -30.0

.326 .522 -30.0

.321 .522 -30.0

.317 .522 -30.0

.313 .522 -30.0

.309 .523 -30.0

.306 .523 -30.0

.302 .523 -30.0

.299 .523 -30.0

.295 .523 -30.0

.292 .523 -30.0

.289 .523 -30.0

.286 .523 -30.0

.283 .524 -30.0

.280 .524 -30.0

.277 .524 -30.0

.275 .524 -30.0

.272 .524 -30.0

.270 .524 -30.0

.346 1.800 4.63

.346 1.800 4.63

.345 1.800 4.63

.345 1.300 4.63

.345 l.faOO 4.63

.345 1.800 4.63

.345 1.800 4.63

.345 1.800 4.63

.345 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.344 1.800 4.63

.343 1.800 4.63

.343 1.800 4.63,343 1.800 4.63.343 1.800 4.63.343 1.800 4.63.343 1.800 4.63,343 1.800 4.63.343 1.800 4.63

-.04 3.11 286.50-.03 3.27 302.52-.03 3.42 319.31-.03 3.56 336.82-.03 3.70 355.04-.02 3.83 373.93-.02 3.96 393.48-.02 4.09 413.66-.02 4.21 434.47-.02 4.33 455.87_.O2 4.M 477.86-.02 4.56 500.41-.02 4.67 523.53-.02 4.77 547.19-.02 4.88 571.38-.01 4.98 596.09-.01 5.08 621.31-.01 5.18 647.03-.01 5.28 673.25-.01 5.38 699.95-.01 5.47 727.12-.01 5.56 754.76-.01 5.66 782.86-.01 5.75 811.41-.01 5.83 840.40-.01 5.92 869.84-.01 6.01 899.70-.01 6.09 929.99-.01 6.18 960.71-.01 6.26 991.83-.01 6.34 1023.37-.01 6.42 1055.31-.01 6.50 1087.65-.01 6.58 1120.39-.01 6.66 1153.51-.01 6.73 1187.03-.01 6.81 1220.92-.01 6.88 1255.19-.01 6.96 1289.83-.01 7.03 1324.84-.01 7.10 1360.22-.01 7.18 1395.96-.01 7.25 1432.06-.01 7.32 1468.51-.01 7.39 1505.31

14

At this time it apoears more attractive to consider a gas stripper although afoil stripper should not be completely ruled out.

Beam Line from RFQ to DTL

Ideally a transport line should be designed to give the beam a double waist with

minimum radius at the stripper. Such a transport line would require unrealistic

quadrupole lens strengths to fit in the allowed length so we are forced to

accept a simpler transport line. The simplest case involves a beam line with a

single quadrupole of a half period in length, to give:

a final = -a initial

& final = |3 initial

Following the stripper a similar line could be used with a quadrupole strength

reduced to 1/3 or a line with shorter drift lengths. The following is proposed:

drift 1quad 1

drift 2

drift 3

quad 2

drift 4

total length

10.434 cm22.5 cm gradient

10.434 cm

stripper is centered

4.259 cm

22.5 cm gradient

4.259 cm

74.78 cm

31.493

here

-11.457

T/»n

T/m

This line gives a beam at the stripper with a radius of 5 mm and a divergence of

8 mrad. Note that this is not optimum for a foil stripper but gives only a very

small increase in multiple scattering with a gas stripper. The question of

whether suitable apertures can be added for differential pumping will be post-

poned as details of this line remain to be calculated; at this stage it is

sufficient to show that the transport and stripping are not impossible. The

transport line is shown in Fig. 1.

15

Drift Tube Linac

The drift tube linac must operate at the same frequency as the RFQ, or at a

multiple of it, so the choices are 23, 46 or 69 MHz. (Frequency steps of more

than a factor of three between the RFQ and succeeding linac are not feasible

because of the relatively large phase spread of the RFQ exit beam.) For such

low frequencies, a structure of the Wideroe principle, which has half the drift

tubes driven by a high voltage rf generator and the interleaved drift tubes

grounded, is more efficient than an Alvarez structure and of smaller diameter.

Such structures, either the more conventional Wideroe linacs at GSI7 or

Berkeley8, or the variation at the Riken Institute9, are characterized by cells

where the separation between successive gaps is n^x/2 where n = 1, 3, 5, etc.

Rf fields in the gaps give a defocusing force to the beam which must be counter-

acted by sufficient focusing (provided by quadrupoie magnets in the grounded

drift tubes) to give stable trajectories for the beam particles. Normally, such

accelerators are designed with n = 1 (TT-TT structure) because this is the most

efficient mode. Sometimes, however, it is necessary to operate the first one or

two tanks as TT-3TT structures (gap spacing of 3ex/2 for the grounded drift tubes)

to provide sufficient length for the quadrupoie magnets.

At 23 MHz, px/2 varies from 7.5 cm at injection to the DTL (60 keV/amu) to 30 cm

at the exit (1000 keV/amu). An investigation with the PARMILA design and

particle dynamics code, showed that an acceptable TT-TT structure could be

designed which had conservative electric and quadrupoie fields in all except the

first few drift tubes where the required quadrupoie strengths are approaching

design limits. A 46 MHz design may be feasible, but would have to be built to

operate in the TT-3TT mode from the input to about the 500 keV/amu point, and

would have poorer acceptance both longitudinally and transversely. Therefore,

for this proposal, we limited the analysis to the 23 MHz design as being a

reasonable and buildable structure that meets the design requirements and pro-

vides a basis for cost and time estimating. However, before committing the

final facility, 46 MHz structures should be further investigated to confirm the

frequency choice.

16

•crnio (N3>

HORIZ

*- 1.3B79

VEUT

1- ?•!•

1- .7(10

EX-I V -

nci24S

. • - •3t— 3. *»B3* • • 3* ie3 « . • • 3* i e

VAMflSLCS* VHLUf1 1*4.33*1 11.4931 42.9*21 -14.37«

MBTCHINO TYPE - 1IESIKES VIH.UES:»L^Mfl-X -1 .9*7»ETB-X .7*1KLPHH-Y 1.9*7IETR-V .7*1

PlISnflTCH FHCTOKS:X-PLBNf *e«Y-PLnNt earn

CODEFILEBATETINE

TRACE I CDC 83»!TROUT*

B" -1

HOKIZ

H- 1

VERT

3»*»

^

sere

•>

,

•«

• ^ - ^ .

761*

X 9«.enRRD

it ana

l

_ _ —

— — ^_

a2

•• ' —

HO« 12

— _

)

• .

VCRT

Sirl»p»r

I1 4

— .

'

a3

—

LENGTH- 743.1

— —

— • -

inn

Fig. 1 Output beam line from RFQ to DTL including stripper.

17

Characteristics of the oroposed OTL are qiven in Table 3. Gap voltages and

quadrupole fields are similar to those in already operating linacs.

Table 3

Drift Tube Linac Characteristics

Frequency 23 MHz

Number of Tanks 8

Input Energy 0.060 MeV/amu

Output Energy 0.265 - 1.0 MeV/amu

Ion Charge/Mass 0.05 - 0.17

Beam Aperture 12.5 - 20 mm radius

Quad Gradients 87 to 24 T/m

Accelerating Gaps/Tank 2 4 - 8

Tank Length 2.4 - 1.6 m

Gap Voltage 116 - 474 kV

Electrically, the DTL is divided into eight independently powered tanks so that

amplitude and phase can be independently adjusted to give energy variability.

For the beam dynamics calculations, each of these tanks begins and ends with a

half drift tube (and half length quadrupole magnet) as if mechanically the whole

DTL were built as one tank with drift tubes number 24, 36, 46, 54, 62, 70 and 78

mounted on solid disks instead of drift tube stems. Actual construction could

be as a single tank, or as 8 separate tanks with full length quadrupoles at each

end. This latter choice would lengthen the entire facility by whatever inter-

tank spacing was chosen, but may be easier to fabricate or align, and could pro-

vide space for intertank diagnostics. If this option is chosen, an intertank

spacing of iiX is recommended to avoid interruptions in the focusing sequence and

excessive longitudinal debunching of the beam.

The DTL tanks were designed, and beam dynamics calculations made using the

PARMILA code. Transit time factors for the accelerating gaps were calculated

with SUPERFISH, which was also used to check that the peak surface field on the

drift tubes was less than 1.0 times the Kilpatrick Sparking Criterion

18

(l*Kp = 6.92 MV/m at 73 MHz). Roth PARMILA, and the companion PARMTEQ code for

RFQ linacs, simulate the real beam with a representative set of particles and

the codes trace these particles through the linac, calculating their

6-dimensional phase space coordinates. For the DTL calculations, a stored set

of particle coordinates from PARMTEQ, adjusted to account for change of charge

state and the emittance growth associated with stripping, are used as input to

PARMILA. For most cases, 360 particles, evenly distributed in phase between

-180 and +180 degrees (dc beam) and randomly distributed in transverse phase

space were used as input for the RFQ calculations. The normalized transverse

emittance for these particles on input to the RFQ was 0.5 -n mm mrad. Calculated

transmission of the RFQ is 86%, so the input for PARMILA was 308 particles

which, because particle loss in the RFQ almost exactly compensated for apparent

transverse emittance growth, also had a normalized emittance of about

0.5 IT mm mrad.

For most of the calculations, the transverse coordinates of the particles from

the RFQ were each multiplied by /2 before starting the PARMILA calculations to

allow for emittance growth in stripping, and mismatches between the RFQ and

DTL. Transmission through the DTL of this 1 n mm mrad beam was 100%. Figure 2

shows the calculated beam characteristics on output from the DTL for the above

conditions. The total energy spread is about ± 1% and the rms spread is

± 0.5%. The addition of a single gap cavity approximately 9 m after the DTL can

reduce this energy spread to < ± 0.1% (rms spread of t 0.025%) as shown in

Fig. 3, which shows the beam at the output of the single gap bucket rotator

cavity.

Output energy can be changed in steps by turning off tanks, starting with the

highest energy tank (tank 8). Continuous variability between these steps can be

obtained by varying the amplitude of the field in the last powered tank- This

procedure works over the range from 1.0 to 0.265 MeV/amu (20 to 5.3 MeV for

singly charged 20 amu ions) by going from all 8 tanks at design field, to only

tanks 1 and 2 at design field and all others unpowered. It is not possible to

further reduce the energy by decreasing the field in tank 2; this introduces too

large an energy spread because part of the beam loses synchronism. (The design

velocity change of the particles in tank 2 is too large for the tank to seem

19

0.04

0.02

0.00

-0.02

-0.04

NCELL = 86, NGOOD= 308, RUN 36680.04

0.02

0.00

-0.02

-0.04-1.50-0.75 0.00 0.75 1.50 -1.50-0.75 0.00 0.75 1.5C

XP VS. X YP VS. Y0.30 i r 1 1 1 1.50

0.15

0.00

-0.15

-0.30

- . • • • ; • *

' • \

W= 20.06

• • • • ; " •

WS= 20.04 PS=-30.00

0.75

0.00

-0.75

-1.50

; . • • • . . \ - \ ' • "

-5.0 -2.5 0.0 2.5 5.0E-EAVG VS. PHI-PHIS

-1.50-0.75 0.00 0.75 1.5CY VS. X

Fig. 2 Beam characteristics at output of DTL.

For description of scales see page 38.

20

0.04

0.02

0.00

-0.02

-0.04

NCELL = 86, NGOOD= 308, RUN0.04

0.02

0.00

-0.02

-0.04-1 .50-0 .75 0.00 0.75 1.50 -1 .50-0 .75 0.00 0.75 1.5C

XP VS. X YP VS. Y0.050 i—, . , , 1 1.50

0.025

0.000

-0.025

-0.050W= 20.06

' i ' • ' -

WS= 20.04

. • •

PS=-30.00

0.75

0.00

-0.75

- 4 0 - 2 0 0 20 40E-EAVG VS. PHI-PHIS

-1.50

• " . . : • • • • ? ? •

-1.50-0.75 0.00 0.75 1.5CY VS. X

Fig. 3 Beam characteristics after single gap bucket rotator cavity.For description of scales see page 33.

21

l i k e a single gap cavi ty. ) However, i f i t is necessary to get down to

0.2 MeV/amu, tank 2 could be sp l i t in two and the f i e l d in the higher energy

section varied as above. The results of successively reducing the f ie lds in

tanks 8 to 3 are given in Table 4. Energy spread increases somewhat as the

tanks are operated at intermediate f i e l ds , but because of the shortness of the

Table 4

Variation of Output Energy as the RF Field in the DTL Tanks is Varied

(particle energy in MeV/unit charge)

(FIELD)/(DESIGN FIELD)TK3 TK4 TK5 TK6 TK7 TK8

WMIN WMAX DW WAVG DWAVG DWRMS

1.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.0.8.6.4.20

111111111111111111111

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.0

.8

.6

.4

.2000000

1.01.01.01.01.01.01.01.01.01.01.01.01.01.01.01.0.8.6.4.200000000000

1.01.01.01.01.01.01.01.01.01.01.0.8.6.4.20000000000000000

1.01.01.01.01.01.0.8.6.4.2000000000000000000000

1.0.8.6.4.200000000000000000000000000

19.80819.31718.77418.18717.56316.92416.48015.92815.31014.68614.08213.64013.14912.62412.08411.55211.22010.81610.3689.8809.3979.0698.6408.1827.7287.3117.0296.6386.1465.6625.289

20.19.19.18.17.17.16.16.15.14.14.13.13.12.12.11.11.10.10.9.9.o#&'.8.8.7.7.6.6.5.5.

273702092454793129613066536980405987512993448900470999503993503216872480055626261798273765371

.465

.386

.318

.267

.230

.205

.133

.138

.226

.294

.323

.347

.363

.369

.364

.347

.251

.182

.136

.112

.106

.147

.233

.297

.328

.315

.232

.160

.127

.103

.083

2019181817171616151414131312121111101099988777665,5,

.061

.532

.952

.331

.686

.035

.550

.013

.437

.840

.243

.809

.324

.799

.255

.715

.338

.906

.432

.938

.449

.127

.751

.333

.896

.471

.160

.725

.213

.716

.334

.0762

.0676

.0592

.0514

.0446

.0393

.0218

.0161

.0241

.0333

.0379

.0459

.0533

.0590

.0616

.0603

.0479

.0354

.0247

.0181

.0158

.0157

.0280

.0402,0474.0471.0401.0299.0211.0162.0141

.0956

.0840

.0728

.0626

.0541

.0478

.0273

.0214

.0329

.0447

.0502

.0595

.0681

.0744

.0771

.0753

.0591

.0431

.0303

.0228

.0202

.0215

.0371

.0520

.0606

.0600

.0499

.0365

.0265

.0207

.0177

22

tanks, this spread is tolerable and can be reduced to the order of ± 0.1% with

two single gap cavities. The one cavity discussed earlier, 9 m after tank 8, is

sufficient to reduce the energy spread as the fields in tanks 5 to 8 are varied

(1.0 to 0.5 MeV/amu), and a second cavity immediately after tank 8 maintains

good energy resolution down to 0.265 MeV/amu.

Variation of output energy and energy spread with bucket rotator cavity phase

and field is given, for the reference 1 MeV/amu case, in Tables 5 and 6. Only

one of the single gap cavities need be powered to reduce the energy spread.

However, it would be advisable to consider simultaneous use of the other cavity

either to fine tune the energy or possibly to reduce the spread further.

Table 5

Variation of Output Energy and Energy Spread

as the

REBUNCHERGAP IW

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

.45

PHI

103133163

-167-137-127-107-97-87-77-67-57-47-37-723538393

Phase of

(particl

WMIN

19.50519.37919.36819.47519.67219.74719.88719.96320.04020.11120.16420.20720.23720.25420.22420.08319.86819.63719.567

the Bucket Rotator Cavity is

e energy

WMAX

20.39420.16119.95719.83819.83819.86519.95420.01420.08220.15620.23320.31120.38920.46220.64120.72120.68120.53420.467

in MeV/unit

DW

.889

.781

.588

.363

.166

.118

.067

.051

.042

.045

.069

.105

.152

.208

.417

.638

.813

.897

.900

WAVG

19.98819.78219.65019.62819.72219.77619.90719.98120.05720.13420.20820.27720.34020.39520.49320.47520.34620.14120.065

charge)

DWAVG

.1538

.1364

.1031

.0629

.0271

.0179

.0075

.0064

.0059

.0051

.0058

.0096

.0170

.0266

.0635

.1040

.1371

.1540

.1551

Varied

EWRMS

.1916

.1702

.1292

.0796

.0352

.0240

.0103

.0083

.0075 ** BEST

.0067

.0080

.0137

.0229

.0346

.0800

.1299

.1708

.1917

.1931

23

Table 6

Variation of Output Energy and Energy Spread

as the Field of the Bucket Rotator Cavity is Varied

(particle energy in MeV/unit charge)

REBUNCHER WKINGAP MV

.70

.65

.60

.55

.50

.45

.40

.35

.30

.25

.20

Low Current Low

PHI

-87-87-87-87-87-87-87-87-87-87-87

Vel

19.95019.97019.99120.01120.02620.04020.02219.99519.96919.94219.915

ocity (3 <

WMAX

20.18320.15820.13420.11020.09120.08220.10320.12420.14620.16720.183

RF

DW

.233

.187

.143

.098

.065

.042

.081

.129

.177

.225

.273

WAVG

20.05520.05620.05620.05720.05720.05720.05820.05820.05920.05920.059

STRUCTURES

DWAVG

.0469

.0382

.0295

.0209

.0124

.0059

.0080

.0156

.0239

.0325

.0412

0.03) Accelerating Structure

DWRMS

.0569

.0461

.0355

.0249

.0149

.0075 ** BEST

.0112

.0207

.0311

.0418

.0525

For the particle dynamics calculations described in the previous section, all

that is really required is a specific arrangement of accelerating and focusing

fields, and these can in theory be provided by various rf structures.

Therefore, although specific accelerator types were assumed to permit the calcu-

lations, in general it is material or physical limitations (practical limits for

magnetic or electric fields for given geometries) and manufacturing consider-

ations that leads one to choose a particular type of RFQ, single gap acceler-

ator, Wideroe or Alvarez linac for a particular frequency and ion velocity.

Therefore, in this section on rf structures, the general question of the

appropriateness of various structure types for different low-3 applications will

be addressed before discussing the specific proposals for the TRIUMF ISOL.

The choice of an accelerating structure for low current, low velocity

(|3 < 0.03), low charge state heavy ions depends on input beam properties

24

(velocity, emittance, size, bunching state, energy spread), desired output beam

characteristics (energy, % transmission, emittance, AE/E) and ultimately on

economics.

If the input beam has relatively low emittance and is bunched, then a drift tube

type structure will be best. As the input emittance increases and a larger

structure acceptance is required, focusing must be introduced to the drift tube

structures. This increases their complexity and usually reduces the structure

efficiency. If the input beam is not bunched and transmission losses cannot be

tolerated, then a bunching structure must be included, further decreasing rf

efficiency.

At some point in the above listed progression of accelerator requirements,

especially as the input velocity is reduced, the optimal choice shifts to a

structure with continuous strong transverse focusing. The radiofrequency

quadrupole (RFQ) is such a structure and has been highly developed in the last

few years. It has a large acceptance, is ideally suited to gentle bunching and

has low transmission losses.

The choice of a drift tube structure for very low input velocity is usually con-

strained by the requirement that the cell length (drift tube length, a^t plus

gap length, g) be equal to 3iA/2. To reduce focusing and accelerating aber-

rations, the acceleration gap, g, must be at least a factor of 4 larger than the

beam hole radius, a. That is, g = 4 ka where k > 1. Then, because i<\ + g =

ii-jX/2 >_ £d + 4 ka, the choice of drift tube aperture places an upper limit

on the frequency. In practice, the RFQ has a similar dependence of frequency on

aperture.

The physical size of the structures varies considerably for a given frequency,

and usually the structure with larger transverse dimensions has lower rf

losses. Thus a compromise is made where capital cost (cost of accelerator plus

rf system) is traded off against operating cost (cost of electricity plus

replacement rf tubes). The latter is a larger consideration for cw machines.

The practical resonators used for very low velocity structures have one common

characteristic - the electric and magnetic fields are each concentrated in

25

different regions of space. This means that even a structure that looks like a

piece of shorted transmission line is, for all practical purposes, a pure

inductor. Thus individual capacitances and inductances can be identified, their

values measured and a reasonably valid lumped equivalent circuit constructed.

Any attempt to use crossed field structures (e.g., transmission lines) for a low

frequency (10 to 20 MHz) structure results in impractically large dimensions.

To minimize the rf power requirement, one should maximize the shunt impedance

per unit length, Zs.

2Q°V

where (C/£) is the capacitance per unit length and Qo is effectively the

quality factor of the inductor. Thus, in the case of separated electric and

magnetic fields,

Zs = TCTTF (RT}

where L is the inductance and R|_ the effective inductor surface resistance.

Therefore, at the required frequency, one wants to minimize capacitance per unit

length and maximize the (L/RL) ratio for the inductor. The latter generally

means that the shunt impedance improves as the inductor transverse dimensions

increase.

Several types of low velocity structures have been designed and can be roughly

classified according to capacitor and inductor configurations, as shown in

Table 7. The IH linac10,11 drift tube configuration is composed of many

parallel plate capacitors, while the RFQ has a long four rod capacitor. The IH

linac and 4 vane RFQ12 structures use long single turn solenoid inductors, while

the 4 rod RFQ 1 3. 1 4 uses individual lumped inductor coils, usually of the one

or few turn type (e.g., single turn15 or spiral16 configuration). The third

type of inductor, used in the split-coax17 and external stub line "Wideroe-type"

RFQ18 is the single turn toroid.

26

Table 7

Classification of Low g Accelerator Structures

According to Capacitor and Inductor Types

Inductor Type

Capacitor Type

Parallel Plate

Long Four Rod

Long Single Turn

Solenoid

Interdigital-H

4-vane RFQ

Single Turn Toroid

Split-coax Wideroe

Split-coax with

modulated vanes,

Wideroe-type RFQ

with external stub

1 i nes

Single or Few Turn

Lumped Coil

Coupled sp i ra l , sp l i t

ring

4-rod RFQ, Wideroe-

type RFQ with

internal stub l ines

The input beam properties and required acceleration characteristics determine

the capacitor type, capacitance per unit length and approximate frequency. The

inductor type should, in principle, be chosen to maximize Q[_, but often a

compromise must be made due to the high cost of large inductors. For example,

the 25 MHz (3i = 0.03) IH structure of Fukushima et al 1 1 requires a parallel

pair of single turn solenoids with 2.4 m diameter. A high power cw water cooled

structure of this size would be complex and expensive to build, but the rf

efficiency might justify it. In constrast, the 12 MHz spiral resonator 4 rod

RFQ structure of Stokes et al 1 9 with 0.35 m diameter spiral wound coils is much

smaller and simpler to build but has a much lower acceleration efficiency. The

advantages and disadvantages of each structure should be weighed for each

situation.

The choice in the present case of the TRIUMF ISOL project would clearly favour a

structure with large acceptance - meaning one with a large aperture and strong

27

focusing. Also, the dc nature of the ion source and the desire for maximum beam

current dictate the use of a buncher system. Only the RFQ can satisfy these

requirements for pi-j = 0.01. However, at the output velocity of Bf * 0.045,

the drift tube structure will provide more efficient acceleration if the reduced

focusing requirements can be met. Thus an ideal structure would be one where

the RFQ input configuration gradually transforms to a drift tube configuration

as the energy increases.

The present design approximates this, first by breaking the accelerator up into

two distinct RFQ and the DTL structures and second by strongly increasing both

the vane modulation and vane-to-vane voltage towards the output of the RFQ. The

low frequency (23 MHz) eliminates both the single turn toroid and single turn

long solenoid as RFQ inductor types, leavinq only some form of single or few

turn lumped inductor.

A 23 MHz CW Four Rod RFQ with Graded Voltage

A four-rod RFQ, constructed of modules (Fig. 4) similar to those discussed in a

previous paper1L* seems suited to the TRIUMF ISOL requirements. The rf

efficiency is reasonable, construction and assembly are relatively

straightforward and the cost should be modest.

Beam dynamics calculations demonstrate that an acceptable design is obtained

with a 23 MHz, 9,2 metre long structure whose bore radius and vane-to-vane

voltage vary between 5 mm and 38 kV at the input and 12.5 mm and 97 kV at the

output. The simultaneous variation of bore radius and voltage allows the output

energy to be obtained with a shorter structure, although a price is paid in

increased rf power requirement.

Some possible advantages of such a four-rod system are listed below:

(1) There is very little current flow between the inductor and the outer

cylindrical tank. This means that, even in a cw system, a demountable

mechanical joint (garter spring or "C"-seaD at the inductor base could be

used to allow easy replacement and service of modules.

28

(Ct>

Fig. 4 A four-rod RFQ module, based on single turn lumped inductors,

(a) single inductor, (b) balanced inductor.

29

(2) When correctly tuned, each four-rod assembly module acts as an inductivelycentre loaded half wave transmission line resonator - meaning there are nolongitudinal currents at the rod ends where the rods from the next modulemake contact. This means that, in practice, only small longitudinalcurrents flow over the rod-to-rod contact and, again, a demountablemechanical joint could be used.

(3) The configuration is automatically "strapped" and well stabilized againstazimuthal electric field asymmetries. The inductors connect opposite vanesvia a very low inductance path.

(4) The maximum magnetic field on the tank wall is only a few percent of themaximum magnetic field on the inductors, and is generally less than onepercent. This means that the surface heating power on the tank is very lowand that only minimal (and possibly no) outer tank cooling is required.This leads to substantial construction cost savings.

(5) The dimensions of the outer tank have very little influence on thestructure frequency, so that dimensional tolerances on the tank can be veryloose, again reducing cost. The outer shell does little else than providea vacuum jacket.

Equivalent Circuit Modeling with RFQ3D

The first step in arriving at the present design was to model the proposedstructure with the equivalent circuit code RFQ3D20. The code input consists ofa specification of shunt capacitance and shunt inductance between each pair ofrods as a function of axial position and the lumped constant values of theterminating inductances and capacitances. The code determines both the vane-to-vane (rod-to-rod in this case) voltage and the longitudinal current flowingalong each rod. The transverse (shunt) current flowing on the inductors is afunction of the transverse voltage and frequency. Because the 4-rod segmentsare acting as sections of TEM line, the voltage is not constant betweeninductors (see ref. 10). The "ripple" in the longitudinal voltage shown inFig. 5 represents a known, reproducible ± 5% variation in vane voltage around

30

Longitudinal Currents0.5

0.4

0 . 3

Cur

rent

B 0 0

<«£ -o.i

-0.2

-0.3

1

; /

/

5 -A

1 r

' /

/

/

jII

-3 -21

I//

I

1

i 1 1 1

A

1I

j

I

/j

1

- 1 0 l 2 ajOneitudinal Posil.iun

-1 -

/

/ -/

-

4 5

60

50

v 40

30

20

- 5

Vane Voltages

2 - 1 0 1 2Longitudinal Position

Fig. 5 RFQ3D calculations of the longitudinal vane current (upper) and thetransverse vane-to-vane voltage (lower) as a function of position alonga modular, 9.2 m long 4-rod RFQ. All five inductors have the samevalue, L = 200 nH. The voltage t i l t is caused by the decrease in vane-to-vane capacitance between input and output ends - 30.8 pf/m to2E.2 pf/m.

31

the average, and such variations could be input to PARMTEQ to fine tune the beamdynamics.

For this analysis, five inductors were assumed as being the minimum to give

acceptable vane voltages. More inductors might be desirable for more rigid sup-

port of the rods, especially if the modules were constructed and aligned in

pairs.

For a constant longitudinal voltage device, identical modules can be horizontal-

ly stacked one after the other, joining the rods at the midpoint between the

inductors where the longitudinal current (the current across the rod-to-rod

joint) is, in principle, zero. The calculations with varying lumped inductances

(Table 8) to produce a tilted field (Fig. 6) show that the longitudinal currents

do go to zero at some points - but, as one might suspect, not at the midpoints

between supports. The breaks in the rods could be made at the calculated zero

points - but it is very likely that by varying the inductor spacings and values,

a tilt can be obtained with the zeros at regular spacings to simplify con-

struction.

Table 8

Estimated Values of Lumped Inductors

required to produce 2.5 x Voltage Ramp

Z (metres)Inductance (nanoHenries)

0.92136

2.76168

4.6200

6.44232

8.28264

The rods would undoubtedly not be circular pipes, but would incorporate the

features shown in Fig. 7. The vane tip blank, looking much the same as a four-

vane structure, would probably have a stainless steel rib brazed to it and

include a copper cooling channel. The machining of the profiles would be done

on a standard NC machine in the modular lengths. Fingerstock or silver braid

should make reasonable rf joints between the rod ends, as was proven on the ATS

32

Longitudinal Currents

>a

w -

0.3

0.2

0.1

0.0

-0.1

-0.2

0.3

0.4

0.5

-0.6

1 T 1 ~~\ 1 "—1

- 5 - 4 - 3 - 2 - 1 0 1 2Longitudinal Position

Vane Voltages

- 5 - 4 - 3 - 2 - 1 0 1 2Longitudinal Position

Fig. 6 RFQ30 calculations of the longitudinal vane current (upper) and thetransverse vane-to-vane voltage (lower) as a function of position alonga modular, 9.2 m long 4-rod RFQ. The vane-to-vane capacitance varies asin Fig. 5. The five lumped inductor values increase towards the outputend, the values being 136, 168, 200, 232 and 264 nH.

33

OFHC Copper

Stainless Rib

Copper tube forcooling

Fig. 7 Cross-section showing proposed rod construction,

including strengthening rib and cooling channel.

34

linac at Los Alamos (although at low duty factor). The oblong rod shape will

have a capacitance intermediate between the « 23 pf/m of 4 rods and the

« 34 pf/m of a 4 vane structure. A rough estimate of the mean capacitance is

28 pf/m with ± 15% variation over the whole length, being high at the input end

and lower at the output end.

An estimate of the individual inductance for each of the five inductors was

obtained from RFQ3D. Assuming a single inductor between vanes in a configuration

similar to Fig. 4(a), the value is « 200 nanoHenries. If a balanced configu-

ration is used as in Fig. 4(b), the inductance is doubled to « 400 nH. The

configuration in Fig. 4(b) would have twice the outer diameter and a somewhat

(although not dramatically) improved "Q".

Lumped Inductor Design and RF Power Requirements

The Q of the system, and hence the power requirements, is determined primarily

by the Q[_ of the lumped inductor, given as

0 —\ R

Once the inductor size and shape are established, a value for RL may be esti-

mated.

The single inductor design (Fig. 4(a)) was chosen on the basis of small size and

simplicity. If power estimates for it are acceptable, then the more efficient

but larger dual-inductor design need not be considered. The calculations showed

that five different inductor values were required, centred around a value of

200 nH. A single turn loop with diameter D = 0.26 m and made of tube with

diameter d = 0.06 m has approximately the required inductance value.

The inductor resistance, Rj_, may be determined by integrating the "effective

rf surface resistance", Rs, over the coil surface.

35

and for pure OFHC copper at 23 MHz, Rs « 1.24 * 10"3 ohms. (The average power

lost per unit surface area is given by 1/2 Rs Jeff2«)

The inductor resistance is given approximately by

RL " Rs * ml " 5>4 * 10"3 ohms

The quality factor of the individual inductors is thus given by

Q, - IT1 « 5300 at 23 MHz.

Consider the power requirements of a single module of length a:

The power loss on an inductor, P|_, is given by

P, = -^r± = Vn2UCT)2 u)2 L = v 2 T ( L}L 2 p T 2 p 2 w L

where ip and Vp are the peak current and voltage, C T is the total rod-to-rod capacitance per unit length, u>2 = l/(L*ACJ) , and ip =

The shunt impedance per unit length is thus

V n2 20.

T Power Loss/Unit Length

For pure OFHC copper, and with Cj = 112 pf/m, the theoretical shunt impedance

is

Zj • 0.65 Mfl/m.

A realistic shunt impedance, taking account of losses on the rods and at the

rod-inductor joint, is probably 30 to 50% lower.

36

Assuming a shunt impedance of 0.40 Mn/m, the total power needed to establish the

required 38 kV input voltage with a linear ramp to 97 kV output voltage over a

9.2 metre length is given by

9'2 Vi

9-2 V. 2

7 in * (1.8)

V. = 38 kV= 108 kW { ,in_ „ Ar

Increasing the number of inductors to six or more (three or more dual inductor

modules) would increase the Q and the outer tank size, but would reduce the

inductor cooling requirements. An eventual choice could be made on the basis of

size, complexity and cost.

Drift Tube Linacs

Any of the previously mentioned Wideroe family linacs7,8,9 have suitable rf

characteristics for this application and the final choice should be based on

ease and economy of manufacture. For the analysis, it was assumed that the

structure was similar to the RILAC heavy ion linac at the Riken Institute9

because such a structure is being operated cw and is characterized by an almost

constant inter-gap voltage, making it easy to check aspects of the beam

dynamics. However, the variable frequency option possible with this type of

structure is not required for the TRIUMF application and changes to the beam

37

dynamics for a GSI or LBL type Wideroe structure would be small, so the ultimate

choice of structure is outside the scope of this report.

Bucket Rotator Cavities

No attempt has been made in this report to specify the type of structures to use

to decrease the energy spread, except to show that the required decrease is

possible with two 23 MHz single gap structures which are capable of gap voltages

up to 450 kV, similar to that in existing Wideroe linac gaps7. Some form of

re-entrant quarter wavelength cavity could probably be used, but the possibility

of doing the bucket rotations with the much easier to fabricate double gap

spiral loaded cavities should first be investigated.

CONCLUSIONS

A linac based on existing or modest extensions to existing heavy ion acceler-

ator technology, could be built to satisfy the TRIUMF ISOL requirements. The

proposed design provides maximum intensity for ions up to mass 20 amu, and with

a single strioper, can accelerate mass 60 amu ions to 1 MeV/amu. Energy varia-

bility from « 0.25 to 1 MeV/amu with resolution better than 1 part in 103 is

provided. Lower energies could be provided by further dividing the first two

drift tube linac tanks (four « 1 m tanks in place of the two » 2 m tanks of this

proposal).

ACKNOWLEDGEMENTS

The many suggestions, critical appraisal and design assistance provided by

Harvey Schneider, TRIUMF, is gratefully acknowledged.

38

Abbreviations in Computer Generated Tables and Figures

A - RFQ beam bore hole radius in (cm)

B - focusing parameter (dimension!ess)

BETA - particle velocity

CAPA - acceleration parameter (dimensionless)

CL - cell length in (cm)

DW - total energy spread (MeV)

DWAVG - average energy spread (MeV)

DWRMS - rms energy spread (MeV)

E - particle energy = W

EAVG - average particle energy = WAVG

EZ - accelerating gradient (MeV/m)

GAP MV - gap voltage (MV)

M - vane modulation factor

NC, NCELL - cell number

NGOOD - number of good particles

PHI - particle phase (degrees)

PHIS, PS - synchronous phase (degrees)

RFD - RF defocusing (dimensionless)

T - transit time factor

TK - tank number

TL - total length (cm)

V - intervane voltage (MV)

W - particle energy (MeV)

WAVG - average energy (MeV)

WMAX - maximum energy (MeV)

WMIN - minimum energy (MeV)

WS - synchronous particle energy (MeV)

X - particle x-coordinate (cm)

XP - particle x-divergence (radian)

Y - particle y-coordinate (cm)

YP - particle y-divergence (radian)

39

REFERENCES

1. H.R. Schneider, B.G. Chidley, R.M. Hutcheon and G.E. McMichael, "A

Conceptual Design of a Linear Accelerator for Radioactive Ions at TRIUMF",

Proc. 1985 Radioactive Beams Workshop (to be published).

2. J. Crawford and J.M. D'Auria, "Proceedings of the TRIUMF-ISOL Workshop",

TRIUMF Report, TRI-84-1 (1984).

3. W.D. Kilpatrick, "Criterion for Vacuum Sparking Designed to Include Both RF

and DC", Rev. Sci. Instr. 28, No. 10, 824 (1957).

4. J. Ormrod, private communication.

5. J. Lindhard, et al., Mat. Fys. Medd. Vid., Selsk 36, No. 10 (1968).

6. P. Sigmund and K.B. Winterbon, Nucl. Inst. and Meth. JJ^, 541 (1974).

7. K. Kaspar, "The Prestripper Accelerator of the UNILAC", Proc. 1976 Linac

Conf., Atomic Energy of Canada Limited, Report No. AECL-5677, 73 (1976).

8. J. Staples, et al., "A Wideroe Pre-accelerator for the SUPERHILAC", ibid.,81.

9. T. Tonuma, et al., "Beam Dynamics of IPCR (RIKEN) Heavy Ion Linac", ibid.,

1031.

10. T. Weis, H. Klein and A. Schempp, Proc. 1983 Part. Ace. Conf., IEEE Trans.

Nucl. Sci., NS-30 (4), 3548 (1983).

11. T. Fukushima, et al., Proc. 1981 Lin. Ace. Conf., LA-9234-C, 296 (1981).

12. J.E. Stovall, K.R. Crandall and R.W. Hamm, Proc, 6th Conf. on the

Application of Accelerators in Research and Industry, Denton, Texas, 1980,

IEEE Trans. Nucl. Sci., NS-28, 1508 (1981).

40

13. A. Schempp, et al., Proc. 1984 Lin. Ace. Conf., GSI-84-11, 100 (1984).

14. R.M. Hutcheon, ibid., 94.

15. H. Klein, et al., Int. Symp. on Heavy Ion Ace. and Applications to Inertial

Fusion, Tokyo, 1984.

16. A. Schempp and H. Klein, "Spiral Loaded Cavities for Heavy Ion

Acceleration", Proc. 1976 Linac Conf., Atomic Energy of Canada Limited,

Report Mo. AECL-5677, 67 (1976).

17. R.W. Mueller, et al., Proc. 1984 Lin. Ace. Conf., GSI-84-11, 77 (1984).

18. A. Moretti, et al., Proc. 1981 Lin. Ace. Conf., LA-9234-C, 197 (1981).

19. R.H. Stokes, et al., Proc. 1983 Part. Ace. Conf., IEEE Trans. Nucl. Sci.,

NS-30 (4), 3530 (1983).

20. R.M. Hutcheon, ibid., 3524.

-41-

APPENDIX A

PARMTEQ input and output for the reference design RFQ. The 308 outputparticle coordinates are retained for subsequent input to the drift tube linac.

RUNTITLE22 30 .40 ,FREQ= 23.00 MHZ, Q=1.0,VI= .060,WF= 3.60 AMU=60.00 1= 0.0MALINAC 1 .060 23.00 60.00000TANK 1 3 .600 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0ZDATA - 5 - 4 . 7 7 6 .232 - 9 0 . 0 0 0 1.000 .038

0.0 4.635 -90.000 1.000 .038 5ZDATA -5 0.000 4.635 -90.000 1.000 .038

18.290 4.635 -83.958 1.023 .03836.579 4.635 -77.915 1.045 .03854.869 4.635 -71.873 1.067 .03873.159 4.635 -65.830 1.085 .038105.122 4.635 -58.493 1.108 .038127.122 4.635 -53.107 1.135 .038143.907 4.635 -48.958 1.166 .038157.480 4.635 -45.642 1.199 .038168.876 4.635 -42.916 1.236 .038178.698 4.635 -40.623 1.277 .038187.328 4.635 -38.661 1.321 .038195.024 4.635 -36.958 1.370 .038201.970 4.635 -35.461 1.424 .038208.298 4.635 -34.131 1.484 .038219.484 4.635 -31.867 1.622 .038224.480 4.635 -30.891 1.705 .038229.149 4.635 -30.000 1.800 .038 182

ZDATA -5 229.149 4.635 -30.000 1.800 .038351.89 2.935 -30.000 1.800 .061920. 1.846 -30.000 1.800 .097 -1

RFQOUT 05START 1STOP -1ELIMIT .1000INPUT 6 360 .76 6.37 .034123 .76 6.37 .034123 180. 0.OUTPUT 2 -1 33 56 00 01 5 600 5OUTPUT 4 1 33 56 33 01 1SCHEFF 0.0 .0499 .0955 10 20 5 10BEGINEND

00O 13

C-O MOOOOOOOOUON3torONJfOrOt>OI-»l-»h-'l->l-«H->l->l-»l-» p3 t"i« • • « * • • « • • • * • • • • « « • # • « « « • • • • • • • • • • • » • » • • • • » • • • • • • • * » • » » • • > • • • • • • • 2J T^

II W O• O (D

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O D S II W

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II S-S

1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 I 1 1 1 1 1 1 I 1 1 1 1 1 1 I I 1 ! j ! j ! I I I I I I I. l_ L L L L L 1 .1 1 1 .1 1 L ! 1 ]_ ! J. ' 1.. . c o b

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en ot"* ON

fo c/3* t nO ~-JON

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bb6b^6bbb6b6b66bo66oooooo66b6^Mm«Nb^^bbwbôooMal^j(»wQ3c^H01oOlli)w^JHO^bôoôlJlb6ON

ow >

III I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I O O O N

oboMII

or1

oo

e 5

(OI

z zzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzzo»oonooooooooonnoonooooonnonoonoooooononooN;

WIT" . .Z H OTJo n > n n II II II ii II n II n n n n ii n n n II it II ii II II n II n ii ii II n II n II n ii II II II II n o

Z • 50- - - - - - o

ZC3 ociocôooooocitriiriciociocjOOQoooooofriooooocicjcriiTJiriiriciwoooooooooooooooooooooooooooooooooooooooooooot-

vICilOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOII tMIOO ODDODOODDODDDODOOODOOODDDDDDDOaOOOaODODD Crt00 hfl N)O I I > II II II II II II M II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II II OJHO* 70 - E C

H OP0

os

-44-

APPENDIX B

PARMILA input and output for the reference design drift tube linacincluding the input line from the RFQ to the DTL and the output line fromthe DTL to the bucket rotator. This run generated the plots shown inFigs. 2,3.

RUN 0 0TITLETRIUMF DTL-MK5/1 23LINAC 8 1.20533TANK 1 20 -30 .0155COFT .720 10.9

.07 -3.2

.596 -19.

.072 -1.92.10 0.

31.8 -369.TANK 2 20 -30 .0170COFT .750 6.97

.067 -2.1

.588 -13.6

.0748 -1.513.90 0.16.5 340.

TANK 3 20 -30 .0170COFT .740 6.97

.067 -2.1

.588 -13.6

.0748 -1.514.90 0.16.5 340.

TANK 4 20 -30 .0170COFT .780 4.6

.0594 -1.38

.5566 -9.5

.0732 -1.15.65 0.16.39 282.

TANK 5 20 -30 .0170COFT .775 4.6

.0594 -1.38

.5566 -9.5

.0732 -1.16.40 0.16.39 282.

TANK 6 20 -30 .0170COFT .810 3.0

.04 0.

.400 0.

.05 0.7.10 0.16.39 282.

TANK 7 20 -30 .0170COFT .840 2.0

.04 0.

.400 0.

.05 0.7.80 0.16.39 282.

TANK 8 22 -30 .0170COFT .830 2.0

.04 0.

.400 0.

.05 0.8.60 0.16.39 282.

MHZ/J

10.0.0.0.0.0.1u.0.0.0.0.u.10.0.0.0.0.0.10.0.0.0.0.0.10.0.0.0.0.0.1rvV •

0.0.0.0.

u.10.0.0.0.0.u*10.0.0.0.0.0.

0

0

0

0

0

0

0

0

L\J

00000000nu0000u0000000000000000000000nV

0000V00,0,0.0.0.u«00.0,0.0.0.0.

A=60:

0

••

•0•

•

"o#

#

"o.

••0•

'o

'o

'o»1

t

3.0.0.0.0.0.0.3.f\V •

0.0.0.0.u.3.0.0.0.0.0.0.3.0.0.0.0.0.0.3.0.0.0.0.0.0.3.nu.0.0.0.0.r\U-3.0.0.0.0.0.u*3.0.0.0.0.0.0.

Q=3

.9979

9979

9979

9979

9979

9979

9979

9979

>

0

0

0

0

0

0

0

0

85-JUL-30

5.5

16.5

n

8.0

3,10.

4.10.

5.12.

r

D .

15.

715.'

8.

3

.03

• U3

.03

.03

03

U3

U

0

3

3

1

3

3

3

3

1

REF.

11

11

11

11

11

11

11

11

0

0

0

0

0

0

0

0

DESIGN

1

1

1

1,

1;

2.

2.

2.

.25

.50

.50

.75

.75

00

00

00

1

1

1

1.

1.

2.

2.

2.

.25

.50

.50

.75

.75

00

00

00

0

0

0

0

0

0

0

0

10

10

10

10

10

10

10

10

0

0

0

0.

0.

0.

0.

0.

.5

.5

.5

.5

.5

5

5

5

24

36

46

54

62

70

78

86

-45-

CHANGECHANGECHANGECHANGECHANGETRANS 1TRANS1TRANS1TRANS1TRANS1TRANS1TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2TRANS2

1111112345612345678910111213141516171819202122232425262728293031323334

456781311313211313131313131313131313131313121

.95.90.85.80.7510.434 1

1049.810.4344.259-1145.74.25936000.0149

-360050

360050

-360050

360050

-360050

360050

-360050

360050

-360050

360050

-360050

360050

-360050

360050.4510

22.511

22.15-2011101101101101101101101101101101101101101101-871

1111

5 112

'z2222222222222222222222222222212

.25

.25

.25

.25

.25

.250100000000000000000000000000000020

0 00100000

200000000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

-1 1.5

1.0 0.05 -30. 0.05

.040 -40. 0.05

LINOUTSTART 0STOP 87ELIMIT 20.0INPUT 0. 23. 23. 3.0 0.333333 1.0SCHEFF 0 .2 1.25 10 20OUTPUT 1 1 1.5 .040 -40. 0.05 86OPTCON 1.4 0.040 0 0 50 80BEGINEND

-46-

LINOUT SUBROUTINE 9 RUN = 3599 85-08-20

TRIUMF DTL-MK5/1 23 MHZ, A=60, Q=3, 85-JUL-30 REF. DESIGN

TANK NO. 1 LENGTH = 240.36CM

FREQ = 23.0 MHZ BORE RADIUS = 1.25 CM EFIELD =1.55 MV/M

CELLCELLNO.

INIT123456789101112131415161718192021222324

LENGTH =KINETICENERGY(MEV)1.211.2901.3761.4621.5481.6351.7221.8101.8981.9862.0752.1642.2532.3432.4332.5232.6142.7052.7962.8882.9803.0723.1653.2583.351

.5*BETA*LAMBDABETA

.0113

.0117

.0121

.0125

.0128

.0132

.0135

.0139

.0142

.0145

.0149

.0152

.0155

.0158

.0161

.0164

.0167

.0170

.0173

.0175

.0178

.0181

.0184

.0186

.0189

T

.844

.849

.853

.857

.861

.865

.869

.872

.876

.880

.883

.887

.890

.893

.897

.900

.903

.906

.909

.912

.915

.918

.921

.924

OUTPUTCELLVOLTS(KV)

116116116116116116116116116116116116116116116116116116116116116116116116

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

.4

E =CELLLENGTH(CM)

7.7.8.8.8.8.8.9.9.9.9.9.10.10.10.10.10.11.11.11.11.11.12.12.

509762009249483712936156372583791995196393588780969156340522701879054227

3.3508GAP

LE NGTH(CM)

2.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.1002.100

MEV PHIS =QUAD

-30.0QUAD

DEGLENGTH

LENGTH GRADIENT(CM)5555555555555555555555555

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

.500

(KG/CM)-8.0.8.0.-8.0.8.0.-8.0.8.0.-8.0.8.0.-8.0.8.0.-8.0.8.0.-8.

727000727000727000727000727000727000727000727000727000727000727000727000727

(CM)

7.15.23.31.40.48.57.66.76.85.95.105.115.126.136.147.158.169.180.192.204.216.228.240.

512728530172668219775656751573514864985020081336

-47-

-48 -

-49-

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CO 3I I I /-sWOWOWOWOW 75OO II*-O-t>-O-IÔ-t>O4>- ~v.£>£> IO O O O O O O O O O D D U>OOOOOOOOO I H O

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-52-

-53-

-54-

OF THE 360 PARTICLES THAT STARTED THE PREVIOUS RUN, 308 SURVIVED

CELLNO.

RFQT?YTTLAI 1CELLNO.86

CELLNO.

PARTIN

308

PARTIN

308

PARTIN

HEBT 308END

END OF

PARTOUT

308

PARTOUT

308

PARTOUT

308

RUN

RMS,NX

.4171

RMS,NX

.1886

RMS.NX

.4782

3599

EMAX.NX,902

.0341

EMAX.NX,902

.0380

EMAX.NX,90%

.0378

PARTICLE

EMAX.NX,100£

.0490

EMAX.N

x,iobx.0681

EMAX.N

x,io6z.0682

COORDINATES

RMS,N

.4498

RMS,N

.6254

RMS,N

EMAX.NY,90£

.0316

EMAX.NY,90%

.0329

EMAX.NY,96%

.8706 .0327

WERE WRITTEN TO TAPE

EMAX.NY,100X

.0495

EMAX.NY,iob%.0514

EMAX.NY,100%

.0502

4

-55-

APPENDIX C

Emittance plots at the output of the RFQ.

TRIUMF DTL-MK5/1 23 MHZ, A=60, Q=3, VIN=60KEV/A, 85-JUL-30 REF. DESIGNOUTPUT SUBROUTINE NO. 1 308 OUT FOR 360 PARTICLES INPUT TO RFQ-.800 .800

IIIIIIIIIIIIIIIIIIIIIIII

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***

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.020—1IIIIIIIIIIIIIIIIIIIIIII

I **_*** ** *I_** ** ** * IIIIIIIIIIIIIIIIIIIIIIIIIT

- .8000 RUN NO.

* * *** * i* * * ** **** *** ** I* * *

* * * * * * * * * i * ***** ** * ****** *i ** **

* * * * * * * * *** i * ** * **** ** i*

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3499 85-07-31 21.07.05. ( X :

- - - 090• •

, XP ) SPACE

IIIIIIIIIIIIIIIIIIIIIIIIT

.800

-56-

TRIUMF DTL-MK5/1 23 MHZ, A=60, Q=3, WIN=60KEV/A, 85-JUL-30 REF. DESIGNOUTPUT SUBROUTINE NO. 1 308 OUT FOR 360 PARTICLES INPUT TO RFQ-.800 .800

IIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIIII

1IIIIIIIIIIIIIII

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****

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-.8000 RUN NO. 3497 85-07-31 20.52.52. ( Y , YP ) SPACE

.800

-57-

TRIUMF DTL-MK5/1 23 MHZ, A=60, Q=3, WIN=60KEV/A, 85-JUL-30 REF. DESIGNOUTPUT SUBROUTINE NO. 1 308 OUT FOR 360 PARTICLES INPUT TO RFQ

-30.000 30.000

.640—

1111111111111IIIIIIIIIIIIIIIIIIIIIIIIII

111*i

**

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1* ** ** 1 *** * * * * *

*** **i **** * * * * **** * * 1** ** * * * * *

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. 040-1

-30.0000 RUN NO. 3498 85-07-31 20.58.43. ( DPHI , DW ) SPACE

30.000

-58-

APPENDIX D

Emittance plots at the output of the DTL.

GRAPH OF ALL GOOD PARTICLES — OUTPUT OF LINACOUTPUT SUBROUTINE NO. 1 ALL 308 INPUT PARTICLES FROM RFQ SURVIVED-.600 .600

IIIIIIIIIIIIIIIIIIIII**I *IIII*IIIIIIIIIIIIIIIIIIIIIII

1.IIIIIIIIIIIIIIIII

-.007- -IIIIIIIIIIIIIIIIIIIIIIII

***

**** *

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-.007-

IIIIIIIIIIIIIIIIIIIIIIII-I

-.6000 RUN NO. 3499 85-07-31 21.07.05. ( X , XP ) SPACE

.600

-59-

GRAPH OF ALL GOOD PARTICLES — OUTPUT OF LINACOUTPUT SUBROUTINE NO. 1 ALL 308 INPUT PARTICLES FROM RFQ SURVIVED-.600 .600 .600I-IIIIIIIIIIIIiIIIIIIIIIII-IIIIIIIIIIIIIIIIIIIIIIIII-

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-.007—1

* * * * ** * *I * *I* ** *IIIIIIIIIIIIII1

* ** **

-.6000 RUN NO. 3497 85-07-31 20.52.52. ( Y , YP ) SPACE

.600

-60-

GRAPH OF ALL GOOD PARTICLES — OUTPUT OF LINACOUTPUT SUBROUTINE NO. 1 ALL 308 INPUT PARTICLES FROM RFQ SURVIVED-10.000

IIIIIIIIIIIIIIIIIIIIIIIII-IIIIIIIIIIIIIIIIIIIIIIIII-

1IIIIIII ***I * **I *****I ** ***I * *** *

* *I ** **I *

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IIIII1 -.300-


10.000

-61-

APPENDIX E

Phase-Energy plots immediately before and after bucket rotator cavity.

GRAPH OF ALL SURVIVING PARTICLES — IMMEDIATELY BEFORE BUCKET ROTATOR CAVITYOUTPUT SUBROUTINE NO. 1 ALL 308 INPUT PARTICLES FROM THE RFQ SURVICED

-50.000 50.000i : : : : ii : : : .300—

1 1 11 ** 1 11 ** 1 11 **** 1 11 ** 1 11 ** 1 11 *** 1 11 *** 1 11 ** 1 11 *** 1 11 *** 1 11 ** 1 11 **** 1 11 ** 1 11 *** 1 11 **** 1 11 **** 1 11 **** 1 1I ***__I 20.057 1I ** I (MEV) II **I II *I** II I*** II I *** II I *** II I *** II 1 *** II I **** II I **** II I ** II I ** II I * ** II I ** II I ** II I ** II 1 * 1I 1 * 1I 1 * 1I 1 * 1I 1 * 1I I II I II I II 1 . 300 1

-50.000 . . . • • • • 50.0000 RUN NO. 3507 85-08-01 09.22.56. ( DPHI , DW ) SPACE

-62-

GRAPH OF ALL SURVIVING PARTICLES — 10 CM AFTER BUCKET ROTATOR CAVITYOUTPUT_SUBROUTINE NO. 1 ALL 308 INPUT PARTICLES FROM RFQ SURVIVED-50.000

I-IIIIIIIIIIIIIIIIIIIIIIII-IIIIIIIIIIIIIIIIIIIIIIIII-

50.000

-.050- -IIIIIIIIIIIIIIIIIIIIIIII

20.058—1(MEV) I

I1IIIIIIIIIIIIIIIIIIII

.050—1

* *

*****

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*IIIIIIIIIIIIIIIIII


50.000

ISSN 0067-0367 ISSN 0067-0367

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Pour identifier les rapports individuelsfaisantpartie de cette serie nous avons assigneunnumeroAECL- achacun.

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0172-86