Imperial College London 1 3. Beam extraction 3. Extraction of particle beams 3.1 The space charge...

Imperial College London 1

3. Beam extraction

3. Extraction of particle beams

3.1 The space charge limit and Child-Langmuirs law

3.2 External and internal fields in the extractor, laminar flow and pierce angle

3.3 The beam emittance, the acceptance of the extraction system and the conservation of phase space


The extraction of particle beams

The plasma generator and the extraction systems are defining :

• The extracted beam current• The quality of the particle beam (emittance)

Space charge forces in the extraction system and plasma properties of the source limit the beam current.


The space charge limit and Child-Langmuir law

me

J

dz

d

constvJ

zz

zemvz

2

.

)()(

)(2

1

0

2

2

0

2

2

anode cathode

0

+Ze

z=d=-V0

d z

z=0=0

(Poisson)


The space charge limit and Child-Langmuir law

34

0

2

23

0

)(

)(2

9

4

d

zVz

d

z

m

eJ SC

z

(z)

00 d

-V0

no current

low current

space charge limited


Current limits given by the Child-Langmuir law

V0(kV)1 10 100 1000

j 0*d2

(A

)

0.01

0.1

1

10

100electrons

protons

C+

U2+

U+

The total current extractable from an ion source is given by :

•The area covered by the extraction aperture (~ d2)

•Extraction voltage (U3/2)

•Mass of particles (1/m)1/2

•Charge state ()1/2

•The distance between the electrodes (d2)

Under the assumption that the particle source is able to produce this current. For electron sources this is usually valid, for ion sources in general not !


The Pierce method for the design of the extraction electrodes 1

0

),,( 34

0

x

d

z

V

zyx

anode

0 d

x

z=0=0

cathode

z=d=V0

z

unbalanced space charge forces



34

0

34

0

2

22

2

2

2

2

2

2

)(

)0( )Re(

0)(

0

1 with

charge spacewithout

d

jxzV

d

uVuf

fu

fj

u

f

jxzux

f

z

f

jjxzu

anode

0 d

x

z=0=0

cathode

z=d=V0

z

Individually biased electrodes to fulfil border condition



3

434

34

0

34

0

ReRe

sincos

cos ,cos

Re),(

jj

j

ed

edV

je

xz

d

jxzVzx

anode

0 d

x

z=0=0

cathode

z=d=V0

z



13

4cos

and

5.6723

4

0xfor

0

tan

34

02

0

1

1

22

d

V

z

x

zxanode

0 d

z=0=0

cathode

z=d=V0

z

x


Beam extraction, high voltage break down limit and aspect ratio

Break down law:

maximum current density for aspect ratio of :

23

0

2

0

2

23

0

2

9

4

2

9

4

2

9

4

Er

S

m

qeJ

d

rS

U

E

m

qeJ

dEUd

U

m

qeJ

SC

SC

SC

*kS

J SC


Phase space distribution of a particle beam

00

,

),.......,.......(

22

11

6

iii ii

ii iii i

ii

iii

i

iii

iii

iii

iii

ii

ii

NN

N

pq

H

pq

Hvdiv

q

H

pp

H

qvdiv

pp

qq

vdiv

epeqv

epeqr

qpr

Hp

q

H

tpprrH


The beam emittance, the phase space ellipse and the twist parameters

x’

F=

single trajectory

)(')()(')()(2)()( 22 zxzzxzxzzxz

z

x

xenvelope

)()( zzE

acceptance


Phase space distribution and beam emittance

eff

RMSKV

n

ii

iiii

ii

iii

ii

iii

RMS

xxxx

xx

xx

xxxx

222

222

,,


Conservation of phase space

x’

x

x’

x

x’

x

x’

x

focu

sing

Drift


Influence of emittance on focal spot size


Ion beam extraction from a plasma

extraction systempl

asm

a

plas

ma

shea

th

plasmagenerator

spac

e ch

arge

The extractable current from an ion source is limited by :

•Space charge forces in the extraction region

•Plasma density in the source

•Production speed of ions in the plasma

•Diffusion speed of ions from the plasma into the plasma sheath

Plasma sheath : While within the plasma the charges neutralize each other, the plasma itself is biased in respect to the walls to keep an equilibrium of losses between the fast electrons and slow ions. A thin boarder area (plasma sheath) separates the plasma from the outside by an electric field.


Influence of particle density distribution at the extraction aperture on initial phase space distribution

transversal current density profile phase spaceplasma


Plasma density distribution at extraction aperture

Experimental set up Experimental result

Extraction aperture

lens system

aquisition

analysis

window

In praxi the particle density at the extraction aperture is not homogeneous. This will lead to non linear space charge forces within the beam transport.

Redistributions of the beam particles within the beam cause growth of the effective (RMS) beam emittance.


The temperature of the source plasma, the potential depression in the plasma sheath and wall effects (losses of particles) are influencing the

beam emittance.

The transversal (and longitudinal) energy distribution of the beam ions is

defined by the plasma temperature and the plasma potential (electric field in

the plasma sheath)

Losses of beam ions at the extraction electrode further reduces the number of ions

to be extracted.

Wall

Wall

resolution


Real extraction systems and the determination of beam formation

radial space chargelongitudinal

edge particles

Initial angleradial lens

focus focus without space charge

For real existing ion sources usually more than two extraction electrodes (here triode) are used to maximize beam current and to influence the beam emittance.

To calculate beam formation self consistently numerical simulation codes like EGUN, IGUN, PBGUN or Cobra are used.


Influence of beam current and aspect ration on beam emittance


Numerical simulation of H- extraction and transport in the LEBT for SNS using PBGUN and comparison with measured data


Numerical simulation of the extraction of a D+ beam for IFMIF using IGUNand comparison with measured data

Imperial College London 1 3. Beam extraction 3. Extraction of particle beams 3.1 The space charge...

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Transcript of Imperial College London 1 3. Beam extraction 3. Extraction of particle beams 3.1 The space charge...