DESIGN OF A MODIFIED DISK LOADED TYPE
FOR ELECTRIC FIELD FOCUSING
Hiroshi YOSHIKAWA
SR-group, Department of Physics,
Japan Atomic Energy Institute,Toukai-mura, Naka-gun, Ibaraki-ken, JAPANAbstract
A proposal for low emittance beam with amodified disk loaded wave-guide is presented.
The disk loaded type has slant disks, and isused with standing wave of 11 -mode and/or 11/2The influence of the slant disks apmode.
pears to be imbalance between focusing force
and defocusing force in the radial component
The integration of theof electric field.
force in radial direction suggests that focusing effect exists.
At the early stage of acceleration when Sis
smaller than one, this configuration enable tokeep low emittance and suppress emittance
growth. The problem for this disk loaded type
experiment is complexity of configuration, but
Manufacturing techit is not impossible.
nologies become enough to make complex highaccuracy products.
Introduction
In this paper I shall present a proposal of
So-called 'Disk
new disk-loaded wave-guide.
type has typically used for electron
loaded'linac and has been deeply studied.
linac is required higher energy,Recently,higher current and higher luminosity in thefield of high energy physics and materialscience.
other type of cavities had been
Manydeveloped, but this conventional type 'Disk
still has several advantages,
loaded type'Disk
therefor many electron linacs adopt
loaded type all over the world.
The relative advantages of Disk loaded type
is in this simplest structure and spacial
The new type of Disk loaded typethrift.
proposed in this paper may abandon one of theadvantages in exchange for acquisition ofElectric field
electric focusing effect.
has
instead of magnetic field,focusing,
if itfairly merit of low emittance holding,used on the early stage of acceleration.
There are two ways to establish a low emitOne is to compose extra accuratetance beam.
beam optics with consideration of higher ordermodes of magnets and flinging effects. Necessarily, the cost of those magnets is so expensive and the alignment is very difficult. The
other way for producing a low emittance beamis quick acceleration into higher energy,
where the particles are not able to change theMy motivation of this proposal wasvelocity.
appeared in this view point.
Design concept
accelerating
type,
wave
standing
Inelectric field of conventional disk loaded
If thetype deform bunches into cone shape.
center of bunches are just put on a crest ofphase, forward particles receive force offocus and backward ones receive defocusing

focus and defocus are alAfter all,force.
most canceled each other. Furthermore, when aparticle phase slips from crest to synchronous
phase phasepartilentegration of radial comOrdinary,ponent should always be defocus.
the beam was suppressed from divergence by
elctro-magnetic-force with multipole magnets.
If it is possible to deny divergence withthere is a probability ofelectric field,emittance decrease.
The new type of disk loaded type is shownin Fig.2, compared with a standard type of
The cross sectional view consists ofFig.l.
round shape corners for higher shunt impedance, and disks have acute angle for theplane which is vertical to axis. Cause of thisbalance between focus and defocus isangle,
broken, and the electric focusing field enhanced.

Side view of conventional structure of DAW.
Fig.l
This is modified type for high shunt impedanceat SIAC.
1.

Fig.2 · Side view of the electric focusing structure.
Bunches travel from left to right.

Computation
The electric field lines of the structure
which has slant disks are calculated by SUPERFISH on PC. It is not established to obtain
the accurate separatrix of each cell, but approximately enough for field lines.

-101-Numerical model
I present a simple model of the focusing
effect for numerical estimation. Based on theresult of FEM calculation as Fig.3, radial
component of electric field near axis Er is
assumed as (Fig.4):
Er = Er 0 cos ( 1rX I)

400~-----------------------------------------,

30121
2121121·······--·----~----....___________________

1121121.....
·······-······-·

where·:·~·- ...

-Hl121

X = x/D : normalized axial distance-20121and 'n' is the number related with the slant
angle of disks, when disks are perpendicular
to axis the 'n' is one. The condition ofO<'n'<l corresponds that the disks are concave
toward the outlet, and 'n' > 1 stands on thecondition of Fig.2.
This electric field of Jr-mode standing wave
propagates in the disk loaded type and a accelerated electron receives radial electricforce Er(x, t):
Er(x,t)----121t=========~~~·····-~=-:-~..=..,---~--~---(1)·... ·-...

-3121121-40121-l.,---r--r--.,.--....-.......,.--r--;:--.,.--....-.......,.--r--;r--..-"T"""""T'0

121.4

121.2

0.8

0.6
-1.2

1.6

2.1
2.5
2.9
3.3
1.8
2.3
2.7
3.1
3.5
Z <cml
R=0.1 ····· R=0.3 · · · R=0.5
1.4

Fig.3 Mutual magnitude of radial components of electricfield at three different·radius fran axis.

2Er 0 cos [ 7r(x/D) 1 sin wtcD

2fthen---(2)The total focusing effect is obtained as anintegration of X: from 0 to 1.
This equation
under assumption that particle phase is crest
shows curves as Fig.5. It is obvious that thefocusing effect exists. Because that the slant~ype must be use in the beginning of acceleration,
Fig.6 is shown a actual condition=0.85,and the . focusing effect is stillenough.

Fig.4

y = cos(1rX2 ) is shown as a line, andy = cos(1rX) is shown as·a dotted line.
X =x/D, D:axial length of one cell.

ErEvaluation
Using eq.(2), momentum increment of focus
and defocus is calculated by integration, andthe proportion aredP(focus)when

S =1,6.69
dP(defocus)dP(focus)when

S =0.85,=2.86

dP(defocus)

Fig.5 Radial component of electric field, which
received by a synchronous particle as S=l.
The dotted line shows radial component of conventional DAW.

However, in case of the conventional type at.~0.85,
the proportion of momentum increment
is 0.56, namely, it is divergence effect.
Conclusion
This new structure of dis·k loaded typedivides a little part of accelerating field
into focusing field. Therefore, acceleration
efficiency
decreases in comparison with conventional type. Nevertheless positive suppression of emittance is inevitably desire for future accelerators.
Acknowledgment
The author wishes to thank M.Sawamura forassistance with computer codes and wishes tothank the member of SR-group at JAERI with
their grateful support and suggestion.

Er

time

Fig.6 Radial component of electric field, which
received by a synchronous particle as S=0.85.

-102-