Magnetic Field Tolerances for the TRIUMF 500 Me V H-

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MAGNETIC. FIELD TOLERANCES. FOR THE TRIUMF. 500 MeV H- CYCLOTRON. M.K.. Craddock and J. Reginald. Richardson*. University of British. Columbia.
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MAGNETIC

FIELD M.K.

TOLERANCES Craddock University

FOR THE and

J.

TRIUMF

Reginald

500

MeV

H-

CYCLOTRON

Richardson*

of British Columbia Vancouver, B.C.

SummaThe percentage losses quoted above show that in accelerating 100 ~.IA to 500 MeV the power equivalent of 20 ~A.(10 kW) will be stripped; this is the loss for which the shielding is desiqned. At lower energies, however, the electric-stripping falls off very rapidly, beina neoliaible below 400 MeV‘(the lifetime varies iniersely-as approximately the 22nd power of E; thus either smaller losses or larger beams can be obtained (e.g. 300 uA at 450 MeV).

The mass of steel in the TRIUMF magnet will be approximately 4000 tons. In designing this magnet it has been found that there is considerable interplay between manufacturing methods and their tolerances on the one hand, and the tolerances required by beam dynamics on the other. This paper reviews the magnet tolerances needed to achieve adequate isochronism and axial focusing, and limit first-harmonic induced radial oscillations and electric dissociation of H- ions. The possibility of separated turn acceleration is also considered.

Cyclotron

design is basically that which has The cyclotron been described previously.2 The most significant change has been the increase in radius to 311 in. Two factors have made this necessary. Firstly, model studies of the magnetic field showed that more spacing between the steel sectors was required to obtain the magnetic field flutter needed for adequate axial focusing. Secondly, measurements recently made by a TRIUMF visitina team3 at the Rutherford Laboratory 50 MeV PLA Gave shown that the H- lifetime in the electric field range of direct interest (1.9 MV/cm) is a factor 3.5 shorter than had originally been anticipated.

Introduction TRIUMF is a co-operative project of the western Canadian Universities of Alberta, British Columbia, Simon Fraser and Victoria to build a meson source on a scale appropriate to a regional facility. The most suitable design appeared to be a 500 MeV version of the 100 PA H- sector-focused cyclotron This required only a relativeproposed by UCLA.’ ly modest budget and offered several advantageous features for the experimenter: (a) (b)

100% Macroscopic Simple, efficient

leading (c)

(d) (e)

system

to

Continuous External Multiple

Of these strated

duty factor (>99%) extraction

energy variability beam qua1 i ty as good simultaneous beams.

features, experimentally.

all

but

(e)

have

(200 to 500 as internal been

The magnet (Fig. 1) consists of six separate spiral hills, each with its own yoke, and constructed from 5” steel plates; there is no iron in the valleys. The magnet coils are constructed separately for each sector from rectangular aluminum bars extruded with cooling water channels and then joined to form a continuous circular coil. The magnetic forces, are amounting to about 1600 tons between the poles, resisted by the return.yokes and a central support.

MeV)

demon-

The use of H- ions to achieve these all-important experimental beam properties leaves the cyclotron designer with two problems he might as a purist have preferred to avoid by sticking to protons but which can be overcome by brute force. Both derive from the H- ion’s low binding energy (0.755 eV), which allows an electron to be stripped off rather easily; this can occur either by collision with a gas molecule or in the “motional” electric

The vacuum tank, 56 ft in diameter and I8 in. high has to resist a. force of 2600 tons on each cover due to atmospheric pressure. The upper cover is supported by skyhooks from a structural steel frame built into the centre post; the lower cover is similarly attached to the reinforced concrete floor. Access to the tank is achieved by raising the upper cover and resonator together with the upper half of the magnet by means of twelve synchronized screw To obtain rapid pumpdown to operating presjacks. sures the chamber will probably be cryooumped by a liquid nitrogen-shielded 20°K helium line, backed up by tvJ0 IO-inch oil diffusion pumps for hydrogen. In addition both the resonators and the vacuum The upper cover chamber will be bakeable to 140°C. will be sealed by a polyurethane ring.

field ~(MV/cm)

= 0.3

y 8 x $(kG)

seen by the ion in its rest frame as the magnetic field B moves past it with velocity v = Bc. To keep the gas stripping below 8% a vacuum better To keep the electhan 7 x 1Dm8 Torr is required. tric stripping below 12% the magnetic field must not exceed 5.76 kG at 500 MeV. leadina to an orbit radius of 311 in., a factor three larger than for an equivalent proton cyclotron. This large size is not entirely without its advantages; mechanical tolerances are relaxed, turn separation is increased and axial injection is made easier. *On

leave

from

Design

The two-dee radio-frequency accelerating system consists of four quarter wavelength resonators operating at 22.88 Miiz, the fifth harmonic of the ion frequency. These resonators, each made up of 18 sections 35 in. wide, are tightly coupled together by the RF magnetic flux linkage and are driven by a single coupling loop.

UCLA

415

A commercial source of H- ions of the Ehlers hot filament type is available, yielding 2 mA within an emittance of 0.7~ cm rad (eV) li2. These wi 11 be accelerated to 300 keV in an HT set and transported vertically down to an electrostatic inflector which will bend them 90” through the centrepost A buncher will be used to into the cyclotron. sharpen the pulse of injected ions as required.

S --,< 2

The magnetic field of a sector-focused cyclotron is designed primarily to keep the ion beam isochronous and focused within certain limits as it is the field intensity is accelerated; with H- ions further 1 imited by electric stripping. In the following sections we discuss the choice of these various 1 imits, which determine the accuracy to which the specified magnetic field must be achieved. In practical terms this decides the dimensional specifications

(ii)

the extent profitable

(iii)

tolerances and for the magnet; to which pursued;

the precision measurements.

shimming

required

in

f(a)

Our method follows that of Richardson.4 The tolerances quoted are to be regarded as standard deviations of a normal distribution about the specified value (i.e. there is a 32% chance the actual value will lie outside the tolerance limits). They are At first also combined as standard deviations. sight this may seem to run counter to our usual notions that engineering construction tolerances Howhave rectangular probability distributions. ever, most quantities depend on a number of individual measurements, and as their errors are conbined a normal distribution is soon approached.

a2

-

sin

5

1 = 2nv $

f2(,

+c’)

$&

(2)

S :

(sin

sin

af

- sin

The duty factor but not uniquel,, radius over the

ab

= 2 -

D : (af - ub)/2n to S; D’s value range

du

-

sin

the

same for phases; acceleralie within with radius.

ae).

is related may vary

=

[f(o)ls=

(6)

d.

1 phases loss is from 0 to the ratio We . 3. ext rac-

When a spiral ridge cyclotron is tuned up by the the process involves adjusting use of trim coils, the gradient d&‘dr in the radial interval 6r governed by each trim coil in such a way that the phase of the ions is constrained to move through the minimum possible change while being accelerated to final energy. Over each of these small radial intervals Grc

by

I dN XiJz=-g-

(‘8)

To achieve this wi II require some averaging of the steel from different melts over the six sectors, A reand small correction coi Is for each sector. lated requirement concerns air gaps in the yoke, x 0.7 x 10-2 x which must satisfy a tolerance of 20 = to.09 in. transverse to the f ? ux path.

harmonic

for

produced see that

T = Tm(Cm/E)k

therefore

&B(AZ,/Z,)

6-

where k = I + 42.6,‘~ 5’ 22 for In the laboratory ‘rn = 70 usec. loss of ions is given by

be a fraction Xt/Zt Making a Fourier analysis

cos

B1 < 1 G we

amount

nN

6p/p = 6B/?r dee gap, we B1 is given

Because of the very strong dependence of the H- icn lifetime T on electric field E only a narrow band of fields (and hence energies) near the maximum em contribute significantly to the stripping. Over such a region the results of Stinson et al3 may be adequately approximated by

to B1 can come from magnetic the sectors, either chemical origin. Suppose one of the six reluctance greater than that will five.

(21)

2-X-’

Electric

To relate this to the steel permeability g we may make a simple magnetic circuit analysis (as in Ref.4). With the realistic assumptions that themagnet efficiency is about 33%, and that half as much flux passes through the valleys as the hills, we find that Au = -. t-0 7%. --3 Qt (20) -22 zt 1-I

At

2Tn

Leaving the remaining precision to be obtained with the harmonic coils, as for the magnetic defects, the tolerance on the voltage asymmetry may ke set . The equivalent to B1 d 1 G; i.e. AVd/V cl = N.]?stringency of this relation at sma 1 radii is tempered by its decreasing validity; a lower limitmay be taken at N = 5 (r = 25”) where oVd/Vd = 10.5%.

One source of a first harmonic is azimuthal misplacement of the magnet sectors. Taking a flat field, hard edge approximation, with equally wide hills and valleys (B z SB), and one of the hills displaced by a small angle b9, Fourier analysis gives

where require

‘n

_ J- 6U(r)

EL=4B,16u i;; 71 i7

at radius rm = 3.30 r,(qVd/~m,c2)~ [where rm is the “cyclotron radius”] and then oscillates with decreasing amplitude about 0.65 A,. In our case rm = 106 in. (33 MeV) and 0.65 A, = 28 B, mm/G. If this is to be no larger than the 3.6 mm oscillations inherent in the expected emittance of the beam [28n mm.rad (eV)t], then B1 & 3.6/?-g = 0.12 G. In view of the tightness of this tolerance and of the many constructional defects which can give rise to the design includes 6 x 12 first harmonic effects, correction coils, each with a capability of il0 G. The tolerance required of each defect is I(:’ G; the coi 1s provide the remaining correction.

(4/n)

= 1 ETn

Comparing this with the change by a field step F?EB along the the equivalent field amplitude

(‘7)

m

B1 =

6pn

accurately

energies

3.

is

418

“Pion Facility Negative Ions”, E.W. Vogt, J.R. NS-13, 262 (1966); 1866 Esate”, G.M. Stinson, D. Axen, E.W.

4.

J.R.

Richardson,

5.

J.D.

Lawson,

a High Energy Cyclotron for UCLA, 1864 (unpublished) Richardson, I.E.E.E. Trans. “TRIUMF - Proposal and Cost (unpublished)

W.C. Olsen, Blackmore

(to

W.J. be

McDonald, published)

Prog.Nucl.Tech.lnstr. Nucl.Instr.Methods.,

P.Ford, L,l(1964)

9,

114

(1967)

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0 9d “l_

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_’

8.

I .y

k? 2 I9

\

c

-i

5 kit“I $2 3=; :: E w I-

3

I-. > b .zc I.$,-+~O*Ln ‘\-a3 obx z- Ln ‘; i z k E ,: s 5 ii

> “,’ f

.--+d I 200 m 0 UlL E LA-\Lnco --y&O” oxx 2 +ln z

2 / pi 2 2

4 2 : P e 5 -s:

L A

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419

I ;J 2 ;< n

\

-.m. J---

.-

i

Lx.

. ..\

-...

i

k$ 55 . .-4 ra IL

.-.-... ,-.. I=

2 L --2: ”2.

5 n +

-. w”i & 8’ ;; k

2 j Li 1 2:

sin a

DUTY

FACTOR

-?5.-.- .

100°~--

40

MAXIMUM

-I Lrl Fig. this the

Fig. 3 Extractable D = 0) vs. microscopic total current loss. Radius

r2

.’

2 Hypothetical radial variation of sin u; is independent of starting phase a1 so that accelerable ions lie within a fixed spread S.

CENTRE Fig:

4

Geometry

of

420

a spiral

sector.

RF PHASE

(%) 30 .,

50

-----

.I . ---.I -

60

ANGLE

beam current duty factor

40

70

2‘\~_ I 80

(DEGREES) (relative D, for

to fixed

90