I . .- Permanent Magnet Edge-Field Quadrupoles As Compact

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SLAC-PUB-6058 SLAC/SSRL-0008 February 1993 (SSRL-ACD)

Permanent Magnet Edge-Field Quadrupoles As Compact Focussing Elements For Single- Pass Particle Accelerators *

ROMAN Stanford Stanford Stanford
.

TATCHYN Center Laboratory CA 94309

Linear Accelerator Radiation Stanford,

Synchrotron University,

Abstract
A previously proposed orthogonally asymmetric arrangement of permanent magnet - (PM) material can be made to generate a highly approximate quadrupole field distribution in the vicinity of its symmetry axis. If a small (X 1 cm) device gap is permitted, a relatively small amount, of conmlerically available PM material can generate focussing gradients in excess of 100 T/m. In this article some of the general characteristics of this configuration are examined and applications to the design and construction of ultra-long undulators on single-pass nlachines are considered.

S&mitted

to Review of Scientific

Instruments

* Work supported

by the US Departjment

of Energy

under

contract

DE-AC03-76SF00515

I

., _ ._

.-

-

1. Introduction

The

properties

of axisymmetric in linear

quadrupole

field

distributions are well on is

as focussing known a

elements

or recirculating magnetic be

machines

[1,2]. The current-driven
yoke the has proven to

quadrupole

configured

steel

particularly element

important,

and

perhaps

preponderant

optical machines.

employed

in present-day there are areas can to as

accelerators of field arise iron), pure

and circular
in which

Nevertheless, or design

design

disadvantages material based

complications referred

from utilizing and

permeable methods would

(henceforth on either be flux

alternative magnets

pure

currents to could

or
be be

permanent

generally useful such

considered densities are

preferable, attained. relevantbroad devices has _-

provided One area

comparably in which

considerations particularly design and

currently A of

is that

of insertion exists without defining

devices, in the iron, the

undulators. construction amount of

base

of experience with done and on

both

and

a large

study which are

been

circumstances to undulator

under construction

alternative suitable In

technological

approaches

[3,4,5].
recent work, iron-based been at SLAC a

60

m

long

pure-PM

undulator

with

a -

superimposed lattice has

quadrupole

focussing/defocussing Free-Electron 1). Analytical facets lattice need Laser studies to be

(FODO) @EL) have kept the of

designed [6]

for

applications

(see Figure

shown [7] that the quadrupole yoke e significantly far away from the PM undulator axis in order to prevent

surrounding modifications

undesirable

2

the on-axis a

field

amplitude. large power

At the minimum consumption the required attention out of

full by

aperture

(12 cm), is

significantly in order In of

the

guadrupoles

necessary (115 T/m).

to attain of

focussing gradients
has been given to the

view

this,

possible lattice

us8 could

PM

structures

which

an alternative‘FOD0

be configured. paper the us8 of a previously-disclos8d for this purpose is PM structure As

In this [8] as a

possible in Figure

candidate

examined. pieces

indicated

2, it consists in the

of four

identical

which, a

if distributed quadrupole the bore lies the in

evenly

azimuthal equivalent

direction, to that

would

generate

field

8888ntially

generated

along

of an ordinary the Contiguity lower

iron-based of the

structure.

The basic

difference in to the

pieces which the

(and their
intuitively B Y that field

edge-fields) can

upper

and the

PM-pairs, of be

be seen
in a

underlie.

maximization It should

gradient

x-direction. rearrangement be _ineffectual; by

evident

attempting

similar would field one the a in for of: _

of the pole it would, to poles

facets in

in an iron-based fact, the the d8Cr8aS8 flux

quadrupole the On-axis

gradients of the

helping

channel into

lines directly
In be the

from

contiguous PM of

other. will

SeqU81, to exhibit

proposed number principle certain the e compact 1)

edge-field properties

configuration and potential

shown

advantages
iron-based examples element axes of of

that

could

make

it useful In of

for replacing particular, the

guadrupoles be given

applications. possible focussing and us8

will for

proposed
the ways

configuring (iron/PM) the economy

lattices 2) some

along possible

hybrid

undulators,

improving

3

. :

and 1.

performance

of

the

pure-PM

undulator

structure

shown

in Fig.

2.

Field

distributions

in the PM edge-field

quadrupole

Expressions structure shown

for

the

B,(O,y,O) 2

and By(x,O,O)

components derived:

of

the

in Fig.

(for L --) -) are easily

By(X)

s >

[,tan

-l[c)

- 2tan-lIh

t*s/2)

- tac'[

lgif

]

+ tan

-'[~++,;zl

-

tan-1(xgi2V)

+

taG1[~~g~J];

(1)

._
Bx(y) -

Br
n

(y + g/a2
X w2 + + (y - (h + g/W2 (h + g/W2
x
w

(y + g/212)

(y +
2
+ (y

(h + g/212
+ (h + g/2) I2

- In
(Y -

II

(2)
l

In the vicinity sufficiently derived s =x(O,~,O) 3Y from large, the

of the axis, the

(1xl,lyl

Q( g/2),

and for w
Y

approximate formula8 by

gradients

of Bx and B

can b8

above

4

I

.. _ .

and aB
(x,0,0)

ax
It is 8Vid8nt are that both
to

0th

order

the

gradients as the

in the holds PM

above for an

approximation ordinary hOW8V8r1 away from

constant From the this

and identical,
asymmetry condition of

quadrupole. it is clear

structure, too far the

that

cannot the

persist

the and

axis.

In order

to indicate

extent

to which

vertical away from

horizontal axis for

gradients quadrupole term8 w.
vs.

remain

sufficiently of

similar practical

the

dimensions

interest, for

the higher-order values the of

in 8qU'S. w 2

(3-4) mUSt g/2,

be examined studies equal

practical that

For

nUm8riCal

indicate to within region or

vertical

horizontal

gradients

remain

54% across

an axis-centered homog8n8ity1'

diameter

of S O.lg. with typical

If this sizes

of "gradient

is associated beams

occupation it

diameter8 b8COm88 and

of particle evident effective from

in linear (3)

or Circular (4) could To that be

machines, _extremely prepared th8

8qU'S.

and

compact from

foCUSSing PM

818m8ntS

commercially 8ff8ctiv8ness Set

available of the

materials.

indicate if we we be

remarkable

edge-field w=8cm, of

quadrupole, L=4Ocm, 100

choose find

the parameter that focussing in the

(g=lCm,

h=3mm, in

B,=lT), T/m can

gradients

8~~888

generated

center

of the device. to make at of this the point pieces magnet is with an in at

A natural comparison * orthogonally symmetrized Fig. 2, i.e., with each

arrangement rectangular

depicted placed

permanent

5

. :

9o"

azimuthal

increments For

about

the

z axis, placed

as

the

PO188

of

an

ordinary to and 8aCh

quadrupole. other

the magnet8 the is field

as Cl088 viz., shown

as possible with that given g-w, the by

to .maximize h*g, it

gradients,

assuming

straightforwardly are

SymTtk8triZ8d PM 8Brh/ng2, (4))
l

qUadrUpO18 about half

gradients that

approximately edge-field quad

i.e.,

of the

(cf. eq.

3. PM edge-field

quadrupole

fOCUSSing

1attiC88

It is of interest edge-field To do this Fig. quadrupole both 3), it

to examine (quad)

the

focussing

performance

of the

vis-a-vi8 and

a conventional lattice to

structure. arrangement thin-lens advance _

individually, wi11 be

in a FODO to

(see

convenient

refer

the

approximation per unit lattice _in cell [2].

to the

quadrupole

and the

associated induced

phase

of the betatron

oscillation

by the depicted

Designating equ's. (3) quad by

the and

absolute (4) by

value G[T/ml,

of either th8

of the two length

gradients f of the is

focal

edge-field given

in the thin-lens

(and near-axis)

approximation

simply

3.35E[GeV]

fbl

L [ml G [T/ml

.

2E(g2

t 2gh) (5)

3BrLh

The phase

advance

per unit

cell

is given

approximately

by

6

I

-;

_

;.

_

$ [radl -D/f,
wavelength

with defined

th8

total

phase

advance

for the

entire

betatron

to be 2n rad.

If we now note denominator made than l-2 for Of orders in

that the rang8
eq. (5) can by

of values simple for

of the term

G-in the be

parameter the

selection

of magnitude

greater with

PM edge-field quad
apertures, in we

iron-based recognize and economy the

quads
the

restricted

immediately flexibility example, for

corresponding by the use

increase of the

design
For

implied

PM option. that

referenced quads

FEL design,

we can

estimate

the

40 cm long with

15 T/m

in Fig. 1 could

in principle

be replaced volume

6 cm long

100 T/m edge-field

quads utilizing
of 1888 than
10

a total
cm3.

of magnetic requiring example, the

material shorter

(per quad)

In designs
for [g]), would could _

betatron

wavelengths

(as would
at lower unit

be typical, energies that quad

for shorter-period on the

FELs operated
adVanC8 per

limitation from be the

phase

cell

result also

restricted by

focal

parameters factors
any

of an iron with iron the

extended MOr8 that with

corresponding for

edge-field it is be per

structure. _apparent configured betatron attractive insertion tabulation

g8n8rally, an

giV8n

lattice, could

alternative f8W8r the

PM

structure

easily Cell8

either

or Significantly latter of option the

more

Unit

wavelength, when device the

being

especially along reference, lengths
for

variation

j3 parameter For

the a a

-

length

n88d8 t0 be minimized.
field gradients is given 3, we can and

of attainable of quad again design

focal 1.

broad range
s Referring mechanical

dimensions to Fig.

in Table also by

note the

a

significant field

advantage

permitted

symmetric

7

distribution the ability

about to in

the

axis all

of the

the

edge-field

PM

quad, with

namely, all the

arrange two

lattice

sections

magnet-pairs access to the

parallel d8ViC8

planes, gap.

providing

maximum

lateral

inS8rtiOn

4. Selected

applications

In this

section for some

we examine both hybrid

some and

alternative pure-PM

focussing

lattice

configurations and discuss We first 3 into the

undulator

structures

of their

implications. of imbedding (i.e., a given iron/PM) D the the lattice of Fig. It is the the a the

consider gap of a

the notion hybrid for be pole order as

undulator. gap

intuitively individual proximity non-matching imbedded evident period

evident quads of the period.

that would iron In

fields. of by with of

aperiodically faces to of an the

modulated undulator regularity it in thus

8nhanC8 as

lattice that 2D is an

fields optimal

much

possible, is one

appears the of FODO the

arrangement to 4) on the some and the PM

which multiple

made Au

identical (888 Fig. Based that

integral the PM

undulator over the

period PO18 it is

quads

are of

centered prior us of

faces. 8Vid8nt

obs8rvations quad structure and

the

section, with the

provides rang8

fr88dOm

of matching implying be

D to a wide that

continuous any two

undulator s structures complement

periods, could

virtually relatively

selected t0

optimized

independently

one another.'

8

The faces pole

remaining quad are Taking

issue fields. .flat, Wn2w,

concerns For

the

actual

effect

of

the that far

pole the from

on the faces

simplicity, and

we will

assume

horizontal, TnL, of

sufficiently

saturation. for the

and w%gu,

an approximate gradients is easily

expression G of the

modification quad by the

the

free-space set of images

edge-field viz.,

first

derived,

G-

161Brlh
n

1
t

g@
(g;(g/2)

+ g2/8 + hg/4 t
2, (g$ W (g/2) 1 2,

(6)

(g2 +2gh)

Obviously, pole faces be

for

undulator Paladin but

structures the

with

wedged expressions symmetry

or

curved will
in

(e.g.,

[lo]), if the

derived

general the iron

different, the

appropriate quad

exists

in _

geometry,

loading

of the also

fields

should

perturb to

their

fr88-SpaC8 their the

distributions

symmetrically,
as

helping

maintain

usefulness, magnitude

to first

order,

focussing

elements. under

To examine _th8 eq. For be abOv8

of a typical
if

image-loading (gu=5Cm,

effect g=2Cm,

apprOXimatiOn8,

we

choose

h=Smm), field.

(6) predicts a concavely possible We to

a 15% change curved make in pole

in the face,

PM quad's

free-space

such of

as on Paladin, the loading

it should

the

magnitude the

significantly of being in it

smaller. able to

note,

passing,

evident with the

importance edge-field

attain

small

dimensions

quad

reducing the analytical and * to a given hybrid d8ViC8. We now consider

mechanical

complexity

of matching

soine of

the

implications

of

replacing

the

9

iron two

quad

lattice of

in Fig. Fig.

1 with

PM edge-field two

optics.

In the top of

structures

5 we

show

alternative other OUtSid while has the

plaC8m8ntS

the quad magnet

lattice, array

one inside, and th8 The latter

the undulator requiring advantage a of

gap. larger

option,

substantially generating field, large

quantity

of material, larger

a

prOpOrtiOnat8ly required

"h0m0g8n80u8" or transport

quadrUpOl8 systems formulas, with we and

as may be dynamic

for machines

apertures. verify even that

Based on the abOV8 general
both the attainable quad

can

readily

gradients

materials favorable H-lcm) .

volume for

for the out-of-gap FEL

are still of Fig. 1

extremely (g,=l.Scm;

the

referenced

structure

A potentially using . tuning either

interesting two

possibility in the

that top

could of B.

accrue

from

of the

structures on-axis image field

Fig.

5 is the the

of the undulator by induced this the are

amplitude

(and h8nC8

K-parameter) . _ for doing

fields. on

Two possible the bottom and of

configurations Fig. 5. Again

schematized one for

choosing _wide

left we

simplicity

assuming

sufficiently

magnets, field

readily

d8riV8 an approximation
Bi, as a function

to the modified gap g,, gap 8

on-axis the

amplitude magnet

of the undulator and the vertical

permanent the

block

height

H,

between

iron plates:

-2n(s e Bb B. It8

- ('3, + WI/Au t ..... I . (7)

10

Assuming for example, could either method fields should lattices this enable tuning will

8 is closed.down that using

to its minimum

size,

gt2H,

W8 .see,

undulator

PM blocks with

H=lcm

and +u-8cm
40%.

the modulationof configuration, also

B. by up to approximately it is evident modify that the the image

In

tuning lattice one

simultaneo~usly to eq.. (6).... For

quadrupole

according of course

a particular the combined

application, tuning

attemptto

optimize

of both Should or for

to facilitate prove Of

the r8gUir8d unrealizable, fr88dOm either

undulator

performance.

strategy

additional n88d quad t0 or be

(electrical introduced

mechanical) independently fields. Apart

degree8

Will the

adjusting from the88

undulator

lattice that be

observations,
5 could,

it should

b8 apparent conditions,

the tuning implemented

methods

of Fig.

under

suitable

significantly movement to be

1888

8Xp8nSiV8ly

than

alternative for of or

methods.involving example, ultra-long less. prove

of the undulator

jaws.

This mightK in of the an case octave

particularly requiring

relevant ranges

undulators

tuning

5. Discussion

A number edge-field briefly on * additional for further

of general

issues

related In

to the this

introduction section, field W8

of

the

quad
field

merit

attention. radiation

fOCU8 some

quality,

damage, and

tuning,

possible study.

applications,

8818Ct8d

r8comm8ndations

11

It has generally to attain somewhat than with

b88n

aCC8pt8d

that r8C8nt
quality magnets.

t8ChnOlOgy with The

i8 able

higher pure

field permanent

iron-based quality of

structures commercially of ongoing

available improvement still-evolving

PM material, [ll], and

hOW8V8r, it can

is still be argued

in a stag8 that based be made with on to

special, ultraprecise deliver Thus, could

fabrication and sorting, Comparable

t8ChnigU88 PM8 could

measurements quality the

field

at least

to iron-based depicted

designs. in Fig. 2

for example, in principle pieces.

four monolithic from

magnets sets

be aSS8mbl8d Her8

of much

smaller, the

sorted

rectangular simple more such

it al80 of the

seems

likely quad

that

extremely to be of

planar conducive

structure to

edge-field

could and

prove

enhancing the it with range more

the

implementation

control

techniques

than

complicated noted

orthogonally that the

symmetric

geometry.

Furthermore, even

is to be rather

8ff8ctiv8n888 possible the for

of the PM quad,
. _

low values

of Br, makes further and

the

use

of

a wide that

of PM materials, t8ChnigU88 fields

enhancing components

likelihood _engineering

construction

sufficiently

high-quality of PM8

can be found. applications damage. can be is

A Well-known the sensitivity machines, of

limitation of their

in accelerator to radiation energies,

field

quality at high

Since intense cases to be

linear

especially radiation, minimum its that

generators th8 the product beam

noise

it is 8Vid8nt

that

in many

of the axis

distance maximum the small FEL

of approach operating heights

of a PM quad lifetime will

times we note in our

limited. in

Here

of the

quad

poles,

particular

referenced

structure,

imply

8XpOSUr88

12

not

significantly (dipole) S), mOV8d we

worse

that those
In

experienced

by the

StrUCtUr8'8 (e.g., PO188

primary see could Fig. b8

magnets. have to al80

alternative that the

configurations edge-field from the quad axis It

seen large

rather

distances or

without is also

seriously reasonable' techniques radiation Perhaps edge-field Equ's.

compromising to will damage one expect

economy that to

performance. effective to help

increasingly be developed in a given

engineering minimize the

continue

or its effects
of

configuration. with regard to the

the more relates that gap an of

obvious to of is

questions potential three

StrUCtUr8 (3-4) G, show

its the easily

for

tunability. parameters

primary For

determining we may also G

0ni.y th8 that size

varied. tuning
of

completeness, (both for

note the

additional the region

parameter gradient magnet and

varying could apart . -

and

hOmOg8n8ity) poles evenly

be introduced in the

by pulling

the contiguous Both this

horizontal

direction. which

g are

obviously -

mechanical in _terms

tuning of

motions, and

could

be 8Xp8Ct8d

to be ad8gUat8 number of

precision An

response

time

for a large
of mechanical

applications. discussed possibly smaller fields value, currents e response

alternative is faster the

method

tuning, could

abOV8, attain mass of Only

image-field times

approach, due to 5). the

which

response element by

potentially PM quad -

its tuning to be

(888 Fig. small

If the

need then

varied

amounts

about

a constant "GC~S88W faster

an arrangement in than

Using

818CtriCally be able to

controlled attain even

would, times

principle, an ordinary

(current-controlled) perhaps

iron quad. natural

In considering

further

applications,

the mOSt

13

question

is

Whether machines apart the

th8

proposed

PM

quad rings).

would

be

usable
regard,

on
it

recirculating is clear be given that, to

(e.g., from the of

storage issue

In this

of tuning, of

consideration

must

size

the

region

gradient that or into

homogeneity. to change the

Regarding their

mandatory

tuning

(as on during the

machines injection lattice could

n88d

lattice of

parameters separating

ramping),

possibility pure-PM, 8COnOmiCal would energy. dynamic upper quad. be

quad

tunable-iron, lead to more

and tunable-PM
designs. attainable Regarding aperture

components the

possibly

Ostensibly,

most' dramatic machines that

economization inject at full the

on fixed-energy the region of

field

gradient

homogeneity, set a

'of recirculating Small8gt limited horizontal not8

machines gap

could size by

strong

limit This

to the may in

p8rmiSSibl8 even vs.

of an edge-field the higher-order distributions. large regions (see _

be the

further vertical

asymmetries We might,
. -

field

hOW8V8rl

that even
and quad

at Substantially

of

gradient l), the

hOmOg8n8ity edge-field economical warranting the effects lattice in of

correspondingly can Still be

larger designed An

gaps to

Table _-

deliver

impressive possibility, mitigating th8 quads

and

focussing further field

performance. study and could

additional for employ -

analysis, be to

asymmetries Using to

alternative as

Configuration the
of

alt8rnat81y"rOtat8d Fig. 3. Assuming that

described r8solutions

caption above in

satisfactory

the

issues, the

it is 8Vid8nt of

an intriguing future e machines, nam8ly the rings based on

direction d8V8lOpm8nt

evolution

circular or '*mini" be

of

ultra-compact, t8ChnOlOgy

non-superconducting

could

14

facilitated. Some that final possible applications 1) the into of the PM edge-field easy insertion quad of the the

d888rV8

mention

are:

potentially storage

Sp8Cially-Configured lattice momentum amplitude us8 of th8 functions compaction at desired

sections

rings ,e.g.,

to modulate to the [13]; change p

for special
factor

applications or to

[12],

modulate ring

function 2) the mini-f) for

locations

around

the

and

quad's either

intense on

fOCUSSing or

gradients

to construct machines, e.g.,

sections, accomodating undulators With analytical Optical for

linear

recirculating such as,

small-gap [14]. regard' and to

devices,

micropole

SUbS8gU8nt study t0 be of

r888arCh, the

a

more

detailed
as an

numerical would with 888m

edge-field W8

quad

818m8nt -quads

warranted. field

recall

that

8V8n

symmetric
doublet

distributions, a high degree

a of _

focussing/defocussing . _ astigmatism distributions -advantage [2]. In

can

exhibit the

this

regard, quad could

asymmetric be utilized

field
to

in the edge-field for these and

perhaps Other

certain if the The natural

multi-element rotated” to extended the -

configurations, configuration lattice8 vertical other in

particularly could be 8mplOy8d.

"alternately same applies

machines

featuring emittance

aSymm8tri88 In the88

b8tW88n

vs. horizontal cases, the

functions. in the prove

and perhaps field

asymmetries edge-field quad

higher-order

components e interest.

of the

could

to be of practical

15

6. ACknOWl8dg8m8ntS . Useful research Department of comments was
by

Sherman at

Winick which

are

,acknowledged. Operated Sciences, of by

.This the

'performed

SSRL

is

of Energy, Sciences:

Office'.of -That

Basic Office's

Energy

Division Materials

Chemical,

Division research.

Sciences

has provided

support

for this

16

TableA 3818Ct8d edge-field fOCUSSing gradients G and focal length8 f attainSbl8 in

quadrupol8s~~compos8d
_.

of PM material

with

B,=lT.E-5GeV

s[cml
0.2 0.2

0.2q*

h[cml

2w [cm1

L[cmL

G[T/mL

fCm1
2.3 1.5

0.04 0.04

0.04 0.08

0.4' 0.4

2 2

364 566

0.5 0.5

0.10

0.10 0.20

1.0 1.0

5 5

146 226

2.3 1.5

0.10

1.0 1.0

0.20 0.20

0.20 0.40

2.0 2.0

10 10

73 113

2.3 1.5

2.0 2.0

0.40 020

0.40 0.80

4.0 4.0

20 20

36 56

2.3 1.5

-

4.0 4.0

0.80 0.80

0.80 1.60

8.0 8.0

40 40

18 28

2.3 1.5

4* 8.0 8.0 1.60 1.60 1.60 3.20 16.0 16.0 80 80 9 14 2.3 1.5 -

* diameter

over

which equal.

vertical

vs. horizontal

gradients

remain

-approximately

17

7. Reference8

[II

M. S. Livingston McGraw-Hill, New

and J. P. B18W8ttt York, 1962.

Particle

Acc818rat0r8,

121

E. Regenstreif, Triplets," Academic

"Focusing

with

Quadrupoles, Particles, 353-410.

Doublets,

and ed.,

in Focusing Press,

of Charted 1967.

A. Septier,

New.YOrk,

pp.

[31

R. Tatchyn Insertion No. 582,

and I. Lindau, D8ViC8S 1986'.

eds.,

International Sources,

Conference

on

for Svnchrotron

SPIE PrOC88dingS

141

R. Tatchyn, Workshop

"Soft

X-Ray

Applications,"

in PrOC88dingS Source, 88/02,

of the

on PEP as a Synchrotron eds.,

Radiation No.

R. Coisson p.97.

and H. Winick,

SSRL Publication

[51

P. J. Viccaro, Insertion Workshop

R. Tatchyn, Working

and R. Coisson, Group Discussions

"Summary at the

of the SSRL in

D8ViC8

on 4th Generation of the Workshop

Synchrotron on Fourth

Light

Sources," Light

Proceedings S0urc88, No.

Generation eds., SSRL

M. Cornacchia p. 86.

and H. Winick,

Publication

-

92/02,

[61 s

C. Pellegrini, Tatchyn, Seeman,

J. ROS8nZW8ig, K. Bane,

H.-D.

Nuhn,

P. Pianetta,

R. J.

H. Winick,

P. Morton,

T. Raub8nh8im8r1

K. Halbach,, K.-J.

Kim,

and J. Kin,

"A 2 to 4 nm High

18

1

.

Power

FEL

on th8

SLAC Linac," 1992, Kobe,

presented Japan;

at the to appear

1992 FEL in Nucl.

Conference, Instr.

August

and Meth.

1993;
. .

[7]

R. Tatchyn,

unpublished.
.,’ :

VI

R. Tatchyn,
Tanh-Function' Undulator Workshop

wPreliminary-Thoughts ,_ Insertion,D8ViC8: Filter,"

on a 'Transverse Its Characteristics in Proceedings Radiation No. as an

and EmittanC8 on PEP

of the R. Coisson

as a Synchrotron

Source, 88/02,

and H. Winick,

eds.,

SSRL Publication

p. 244.

[9]

R. Tatchyn, Operation," Generation SSRL

"Optimal

Insertion
of

Device

Parameters

for SASE FEL

in Proceedings Light Sources, No.

the Workshop

on Fourth eds.,

M. Cornacchia p. 605.

and H. Winick,

Publication

92/02,

[lo] G. A. Deis, Rego,

A. R, HarVey,,C.

D. Parkinson,

D. Prosnitz, "A Long

J.

E. T. Scharlemann, Wiggler PrOC88dingS

and K. Halbach, for the Paladin
of

El8CtrOmagn8tiC
Experiment, "

Free-Electron Inernational 23-26,

Laser

the

Tenth

Conference LLNL/UC -

on Magnet Preprint

Technology, .

Boston,

September

1987,

[ll] K. Halbach, m -

private

communication.

[12] A. Amiry

and C. Pellegrini,

"Design

of a Quasi-Isochronous

19

. :

Light

Source,"

in PrOC88dingS Sources, No.

of the Workshop

on Fourth eds.,

Generation

Light

M. Cornacchia p. 195.

and H. Winick,

SSRL Publication

92/02,

[13] M. H. R. Donald, PrOC8edingS
S0urc88,

"Low-Remittance

Lattice

for PEP,"

in Light

of the Workshop

on Fourth

Generation eds.,

M. Cornacchia p. 122.

and H. Winick,

SSRL Publication

No.

92/U,

[13] R. Tatchyn, micropole Rev. Sci.

P. Csonka, undulators Ins&m.

and A. Toor,

"Perspectives radiation

on

in synchrotron 60(7), 1796(1989).

technology,"

20

Fiqure

Captions
‘.

Figure

1. Pure

PM undulator field

design

with

a superimposed

quadrupole

lattice

generated

by iron-based

quadrupoles.

FigUr8

2.

Schematic All axis

of the permanent have their

magnet easy

edge-field

quadrupole. to the y field

four pieces

axes parallel with the

and are identically directed

magnetized,

vectors

as shown.

Figure

3. Parameters composed

of a focussing/defocussing of PM edge-field would quadrupoles.

(FODO)

lattice

An alternative lattice

arrangement in which oriented, . _ the z-axis. the

be to first in each

set up a similar section second were quad

segments

identically by 90' about

and then

rotate

every

_-

Figure

4. Arrangement

of an edge-field

guadrupole with

FODO

lattice poles.

in By

the gap of an insertion centering th8 the quads

d8ViC8

permeable faces

over the

iron pole

and keeping (Or some of each -

same periodicity

as the undulator identical image

StrUCtUr8 modulation

multiple quad's

of it), virtually field by the induced

fields

is ensured.

m

-

Figure

5. Front

views

of

pure-PM

undulator

structures. primary

The large dipole

rectangles

represent

the undulators'

21

arrays.

In th8 upper

tW0

figUr88, pole

alternative pieces

placements

of an edge-field vicinity bottom field

quadrupole's dipole

in the In the

of the primary left figure;

arrays

is shown. the

a method undulator is shown.

for tuning with

on-axis. pure-PM

of a pure-PM lattice the

a superimposed

guadrupole 8 b8tW88n

By changing on-axis induced

the gap height field is modified

iron plates, image

the

by the equivalent An alternative in the bottom

charges

in the plates. is schematized

realization right figure.

of this

method

22

J.
,

I

8cm

Fig. 1

I

:

.

Fig. 2

r

Fig. 3

tY

Fig. 5