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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
8/10/2019 Beam Focusing With Solenoid
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
8/10/2019 Beam Focusing With Solenoid
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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