beam focusing with solenoid

8/10/2019 Beam Focusing With Solenoid

1/4

EXPERIMENTAL STUDIES OF ELECTRON

BEAM

FOCUSING IVITH SOLENOID LENSFS NEAR THE SPACE CHARGE L IMIT*

11. Reiser , 1, . Namkung, p . Loschia lpo , J . Sute r , +

and

J.

D.

Lawson++

+TJnivers i ty

of Maryland,

Col lege

Parl

90

and sextupole

( t h i r d - o r de r )

i n s t ab i l i

t i e s

when 0

0

>

60 .

There

are a l so in tens i ty

thresholds, i.e. lower

l imi t s

for 0/0

0

, t ha t

depend on the

form

of the p a r t i c l e d i s t r i b u t i o n

func t ion and on coupl ing between

t r ansver se and

longi tudinal

modes. For a K-V

d is t r ibu t ion ,

for

instance,

one

has the s t ah i l i t y requirement

0 /0

0

;;. 0.4

and

0

0

< 60 .

In

our exper iment , we

p lan

to vary both

a and a

over

a wide

range

to

cover a l l poss ih le ~ n s t a b i l i t y

modes

pred ic ted by

theory. The use of

gr ids to

accomplish t h i s i s

be ing s tud ied a t the

Rutherford

Labora tory .

Electron

Beam

Apparatus

The three major components

of

the

appara tus

are

the e l ec t r on gun, the solenoid focus ing

system,

and

the d iagnos t i c chamher, as

descr ibed

prev ious ly . 3 The experiment i s

designed

to

proceed in s tages: several e lect ron

guns

producing d i f fe ren t beam cha rac te r i s t i c s wi l l

be

t r i ed ; the var ious beam

pro f i l e s in

f r ee space

are

measured f i r s t ;

then

solenoid lenses wi l l be

added, one a t a

t ime,

un t i l

the

fu l l length

of

the focus ing

channel

approximate ly 30 lenses) i s

completed.

In pJe l iminary

s tud ies with a home-made

Proceedings of the 1981 Linear Accelerator Conference, Santa Fe, New Mexico, USA

235


2/4

electron gun, we measured the free-space

beam

envelope expansion and focusing

with one

and two

lenses .

3

Subsequent

measurements

of the radial

current

density

with

a Faraday

cup revealed

that

the

beam

becomes hollow

when

i t is focused. This

led us to s ta r t

a more

systematic study of the

beam

propert ies with

only

one solenoid

lens.

The

experimental

configuration for

the

measurements

is shown

in Fig. 2.

The

electron

gun

is the

same

as that in Ref.

3,

except that

the

cathode-anode gap

is

only 1.6

cm and the beam

current

is 310

rnA versus

230 rnA a t 5 kV. The

diameter of the cathode is

1

cm and

the

anode

aperture

is covered with a

fine

tunsten

mesh.

The center

of

the

solenoid is

8.6 cm

from

the

anode. A

fluorescent screen at the

end

of

a

hollow tube,

can

be moved along the beam axis ;

the

screen pic tures of

the beam, which

can be

seen through the

tube, are recorded with

the

aid

of

a

TV video-tape

system.

Experimental

Results

The

radial

density

prof i le near the anode,

fluorescent

screen

pictures,

and

the

beam

envelopes for various peak

magnetic

f ields from

o to

380

G of

the

fu l l - s ize

beam

were

already

published in our previous

paper.

3

We

have

now

also measured the

radial

density

prof i les versus

distance

along the axis for various magnetic

f ie lds . Figure

3 a)

shows

three

prof i les at a

distance of 20, 22, and

24 cm,

respect ively, with

a

f ixed peak

magnetic

f ield of Bo

117 G. The

most notable feature is

the hollow st ructure of

the

prof i le

even though

the beam pr ior

to

entering the

lens

has

a

peaked, almost Gaussian,

shape

see

Ref. 3) .

However, i t

appears that

with

increasing distance, the

hollow

feature

gradually

disappears.

The

asymmetry in the

prof i le curves

is

caused by

misalignments

in the

system

and

possibly

some

nonuniformity

in

cathode

emission

We

do not

ful ly understand yet why the

beam

becomes

hollow. However,

quali tat ively, we

at t r ibute

this phenomenon

to

a combination

of

lens aberrat ions, nonlinear space

charge

forces ,

t ra jec tory rotat ion in the

solenoidal

magnetic

f ie ld ,

and

the

relat ively low

temperature

of

the

beam. ~ h e

emittance is

E > rc 12kT/eV

3 x 10- m-rad, where

rc cathode

radius 0.5

cm,

kT cathode

temperature 0.12 eV, V

gun

voltage

5

kV).

From the qual i ta t ive analysis ,

one

concludes

tha t the radial prof i le should be less hollow

when the beam

radius is

reduced since

a l l

of the

mentioned

effec ts

increase

with

radius .

We

therefore inser ted

a

thin

mask

into

the beam

behind the anode, with

an aperture of

0.5 cm

thus

reducing

the beam

size

by a

fac tor of two. An

important addit ional

feature

of the mask

are

two

0.5

mm pinholes outside of the reduced beam

aperture

but

inside of the fu l l - s ize

beam

radius,

as shown

in the upper

lef t

corner of Fig. 4.

e

should

note

that the mask

reduces

the

current

I ,

and hence

K, by a factor of 4 and the

emit tance by a factor of 2. Consequently, in a

periodic

channel ,

the space charge parameter

u

would

decrease by a factor 2 and the tune sh i f t

rat io 0 /0

0

would increase.

Some

experimental resul ts

obtained

with the

reduced

beam

are

shown

in Figs. 3 b), 4, and 5.

Fi rs t , in

Fig.

3 b) , we see, by comparison with

3 a) ,

tha t

the beam prof i le

is considerably less

hollow than

in the case of the fu l l - s ize

beam

confirming our expectations.

In

Fig. 4, the

envelopes for

the reduced beam are plot ted

for

different

magnetic

f ie lds .

Computations

show

that

only

the free-space curve Bo 0) agrees

with the envelope

obtained

from integrat ion of

Eq. 1) . The

phosphor screen, pictures taken

at

a

fixed

axial

posi t ion of

z

16 cm with

varying

magnetic f ie ld st rength,

are

seen in Fig. 5. We

note that

a l l of

the

fea tures discussed

already

in Ref.

3

are present here as well , in par t ic

ular ,

halos

near the waist and images of the

anode

mesh downstream from the

waist . However,

in contras t to

the

fu l l - s ize

beam,

the halos are

less

pronounced

and the images are

sharper.

Of

part icular

in teres t

is

the fact that the

images

of

the

anode

mesh

f i r s t

show

shadows of the

wires; but then, as

the

magnetic

f ie ld

is

increased,

they become br ight .

Equally noteworthy is the behavior of the

two beamlets defined by the

pinholes. Since

they

are

launched

from

a

region outside of the

reduced

beam

radius,

the defocusing

force

due to the

space charge F

I / r )

i s less than on beam

electrons

near

the edge r a) . Thus, the

two

beamlets

enter in to

the beam

near

z 18

cm),

as

indicated schematically in Fig.

4

for the outer

beamlet , b). When the magnetic f ie ld is turned

on

and

increased, the two

beamlets cross

the

axis

and emerge

on

opposite sides of the

beam,

as can

be seen in the photos of Fig. 5. One can

also

see a

coma-like

dis tor t ion of the beamlet cross

sec t ion

In conclusion, we found tha t the beam,

focused

by

only

one

solenoid, shows a var iety

of

effec ts some

of which were unexpected.

While

we

do

have

some qual i ta t ive

explanations, more

experimental studies as well as numerical

simulation wil l be required to

obtain

a fu l l

understanding. Thus, in para l le l

with the

construction of the periodic solenoid

channel ,

we

plan

to

devote some time

to

more detai led

studies

of beam

behavior in

a

s ingle

lens.

With

regard

to

the

periodic

channel ,

we plan

to increase

the

effec t of

emit tance

versus

space

charge, and

thus

the tune

0 ,

by

lowering

the

gun

voltage, decreasing the

beam perveance,

and using

beam

masks and specia l

gr ids. The

f i r s t

resul ts

with the grids at

the

Rutherford Laboratory

are

already quite

encouraging:

i t

was

demonstrated

that

the

beam

radius

can

be

increased

eas i ly by a

fac tor of

two

with proper

grid

voltage and

polar i ty.

References

1.

M. Reiser, W. Namkung,

and

M. A.

Brennan,

IEEE

Trans. NS-26,

3026

1979).

2. M. A. Brennan, Loschialpo, W.

Namkung,

M.

Reiser, and J . D. Lawson, Proc. Heavy Ion

Fusion

Workshop, LBL-10301,

Oct.

1979,

p.

77.

3. W.

Namkung,

P.

Loschialpo, M.

Reiser, J .

Suter, and J . D.

Lawson,

IEEE

Trans. N S - ~

2519 1981).

Proceedings of the 1981 Linear Accelerator Conference, Santa Fe, New Mexico, USA

236


3/4

4.

L. SPlith

et

a1.

BIFAN-13 14,

15, and 43,

Lawrence

Berkeley Lahoratory 1977).

5.

1 . Baher and

A.

\.].

Maschke,

Phys.

Rev. Lett .

42, Hi7 1979).

6.

1- Hofmann IEI F: Trans.

1i

2399

1981).

Fig. 1 Channel acceptance, Eq. 2), and

brightness, Eq. 5),

define

actual

beam current , 1

1

; 1m

0.5 IoS3y3ao/S,

/;)2

beam focusing with solenoid

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