F. Willeke, Snowmass 20011 Luminosity Limitations of e-p Colliders Extrapolation from HERA Experience Examples for IR Layout LINAC-Ring Limitations HERA.

F. Willeke, Snowmass 2001 1

Luminosity Limitations of e-p Colliders

•Extrapolation from HERA Experience•Examples for IR Layout•LINAC-Ring Limitations•HERA Limitations


HERA Luminosity

222222

0

4 yeypspxexp

bep fnNNL

2001 PARAMETERS

Np number of protons per bunch = 1 x 1011

Ne number of leptons per bunch = 3 x 1010

nb number of bunches = 174

f0 revolution frequency = 47.3kHz

x,y,p,e hor./vert. beam dimensions of leptons & protons = 114m/ 30m

half crossing angle = 0

L luminosity = 7 x 1031cm-2sec-1


HERA Luminosity Constraints & Limitations

**2 xpypN

pep

e

INL

Limitations: Np / N proton beam brightness = 1 x 1011/ 4m (injector, ibs, bb-e)

Ie total lepton beam current = 60mA (rf power, bb-p)

p proton relativistic factor = 981 (max field, circumference)

x,y p hor.& vert. Betafunctions at the IP = 2.45m/0.18m (ir layout, p)

Constraints: mr (beam-beam tracking Sen‘95) => set 0(head on coll.)

x,yp=~ x,ye (Brinkmann, Willeke PAC’93)

e not (yet) limiting

L = 7 x 1031cm-2sec-1

To what extend are these fundamental?


Proton Beam Brightness Limitations

Present design Np / N =1 x 1011 / 4 x 10-6 m

Laslett Tuneshift in DESY III Booster Synchrotron 50MeV (kin.energy) injection

sc ~ R Np / ( N B ) = 0.6 @ 1.3 1011 & N=2mCan be overcome by smaller ring are higher injection

energy in the booster

No principal limitation `just´ costs

Example:

DESYIII Inj. Energy from 50MeV120MeV @ 10M$


Proton Beam Brightness Limitations:IBSScaling from HERA

N p 1 1011 E 920 GeV E A 1 920 GeV

3.17 10 4 s 0.12 e volt sec N 4 mrad mm x 0.419 mm

e 7.392 10 5 s 168.386 mm 4.079 nm y 0.419 mm

0.562 ns

longitudinal s h

2

2 e2A ib F c 1 c 2 c 3

1

s 8.238 hour

A ib1

64 2r 0

2 c

s e x y xp yp 4

N p F c1 c2 c3( ) 8

0

1

x2 ln c32

1

p x c1( )1

q x c2( ) 0.577 1 3 x2

p x c1( ) q x c2( ) d

p x c1( ) c 12 x2 1 c 1

2 q x c 2 c 22 x2 1 c 2

2

h1

e2

D x2

x2

D y2

y2

1

d 1 x c 1 h

xpc 2

h yp

c 3 2 h dr 0



Scaling IBS

Increasing Np/N increases growth time:

larger s Larger s larger * (hourglass effect)

Luminosity almost independent of Np/N

Possible Cure: More RF Voltage

ibs~URF0.25 however e ~ URF

0.25

L / L0 = (e / e )2= (URF/ URF0)1/2 (expensive)

HERA Experience: Running with 2x nominal e still ok but effect already noticeable (increased backgrounds)

s~N1.42~s

1.52~URF1/4


Cooling

Bunched Beam Stochastic Cooling at High Energy

Not very promising perspective

Bunched e-Beam Cooling:

-May be cost effective way to provide bright beams

-Doesn‘t look promising for high energies

-May work for ions

See K.Balewski‘s presentation


Lepton Beam-Beam Effect

This is already a rather large value which potentially limits the proton beam brigthness.

What are the margins? beam-beam experiments

*

*

*

**

*

2zp

yp

zp

xpzppNe

zepeez

Nr

ey=0.045


Too Strong Beam-Beam Force on e?

No reduction of Ls by the second experiment

No reduction of Ls by a larger -funktionen

Ls

Ippb

So far no reduction of Ls by the bunch

current


)(mey

measureds ,L

Where are the Beam-Beam Limits?

Upgrade and Ip=140mA: emittance starts to grow

)(mey

yQ2

xQ2

)(mey

emeasuredx,

emeasuredy ,

)(mey

)( ,ecalcys L

measureds,L

)( ,emeasuredys L


Conclusion of Proton Beam Brightness Limitation

For a machine with the circumfrence and the energy range

of HERA there is no large increase factor in p beam brightness possible.

A factor of >2 might be compatible with lepton beam beam effect and controlling IBS

Lepton Beam-Beam Effect: Could be mitigated

By smaller beta, however: D.A. limitations

present HERA optics DA=~15-20 x


Electron Beam Current LimitationsRF RF installation costs, operation costs Not fundamental Now: RF power 12 MW, RS1.5GW 60mA @ 27.5GeVCost example: prov RF to increase I by factor 1.6 5M$

Vacuum costs, not fundamentalSR losses 5.2MW @ 1000W/m (~B-Factories ) Presumably no big current increase factor reasonable! (factor 2-3?) costs!

Feedback System: designed for 60mA, upgrade no technical problem

Proton Beam Beam Effect (stability, background, lifetime concerns)

N

beppx ef

Ir

2

b=96ns, unproblematic

For IR design & paras. Resonancespx=1.4 x 10-3 limit?f: fill factor


Ls is independent of

e-current

Tp depends on e-current

Tails depend one-current

Too Strong Beam-Beam Force on p?16mA 73mACorresponding e-current after upgrade


Conclusions: Electron Beam Current Limitations

Educated guess:

Besides COSTS, the beam current is limited by

IR design considerations and beam-beam effects.

For HERA, the e-beam current could be increased by a factor ~2 if costs could be disregarded


Limitations to Focussing

•Chromatic effects Dynamic Aperture Limitations

•Hourglass Effect

•Interaction Region Layout and IR Magnet Design:

Need e & p lenses close to IP

Crossing angle

separate quickly beam dynamics, geometry

Magnetic Separation

Concern about SR


Lumi Reduction by Hourglass Effect

)(cmpy

ep

75.1)5.12(

0LL cmpyLength

19cm:

12cm: 9.1)5.12(

0LL cmpy

Luminosity ( )3210

20cm

bunch length: 6cm

30cm


New HERA Inter Action Region (==>see M. Seidel)strong magnetic combined function separation

Half Quadrupoles Superconducting Separator/Quads

p-focusing

sc sc

p-beam

e-beam

e-focusing DF p-focusing D-F-D-F


Superconducting Magnets in the Detectors


Ring Linac ColliderBecome interesting at Lepton Energies beyond capability of Storage Rings Ee>100GeV

Np 10-6m p 10cm Pe 250GeVL= 4.8 x 1030cm-2sec-1

1011 N 1066 * 26.6MW Ee

High Energy bunched beam Cooling! Energy Recovery


THERA LINAC-Ring Lattice (proposed) small crossing angleprotons focussed by 2 electron low beta triplets, *=10cm max 8kmprotons deflected from e-orbit by a long off-center quadrupoleelectron orbit straightenergy range Ep/Ee: 4/1 - 1/1

Proton Optics

1TeV

Electron Optics

250GeV-800GeV


Conclusions

• Ring-Ring HERA L=~1032cm-2sec-1 New Collider in the range of HERA

Energies: L=1033cm-2sec-1 is an ambitious goal and may be considered as a target for new designs

• Ring-LINAC L>1031cm-2sec-1 :only feasible witg bunched beam cooling

F. Willeke, Snowmass 20011 Luminosity Limitations of e-p Colliders Extrapolation from HERA Experience Examples for IR Layout LINAC-Ring Limitations HERA.

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