Synchrotron Radiation Dominated Hadron Colliders

EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH European Laboratory for Particle Physics

Large Hadron Collider Project LHC Project Report 102

SYNCHROTRON RADIATION DOMINATED HADRON COLLIDERS

Eberhard KEIL

Abstract

The synchrotron radiation damping time becomes small compared to the beam lifetime when the beam energy in a circular hadron collider reaches about 100 TeV and the dipole field about 10 T. This paper discusses an approach to the design of these colliders such that the desired performance parameters, e.g. beam-beam tune shift and luminosity are achieved at the equilibrium values of the beam emittance and momentum spread. The design procedure is described, involving the design of the interaction regions, the arcs, and the RF system. The thresholds and/or growth rates of several collective effects, and the growth times for intra-beam scattering are estimated. The consequences of the synchrotron radiation are discussed in the conclusions.

Presented at 1997 Particle Accelerator Conference, Vancouver, 12-16 May 1997.

Administrative Secretariat LHC Division CERN CH - 1211 Geneva 23 Switzerland

Geneva, 3 June 1997 SYNCHROTRON RADIATION DOMINATED HADRON COLLIDERS E. Keil, CERN, Geneva, Switzerland

Abstract 2.1 Interaction Region Design

The synchrotron radiation damping time becomes small For round beams with equal normalised horizontal and ver-

= = z

compared to the beam lifetime when the beam energy in tical emittances z , equal -functions and van- z a circular hadron collider reaches about 100 TeV and the ishing dispersion at the interaction point IP, and ignoring

dipole ﬁeld about 10 T. This paper discusses an approach crossing angle and “hourglass” effect, luminosity L and N to the design of these colliders such that the desired per- beam-beam tune shift are with bunch population and

formance parameters, e.g. beam-beam tune shift and lumi- collision frequency f :

nosity are achieved at the equilibrium values of the beam

N f Nr

emittance and momentum spread. The design procedure is p

= =

L (2)

4 4

y n described, involving the design of the interaction regions, x the arcs, and the RF system. The thresholds and/or growth rates of several collective effects, and the growth times for The beams cross at an angle in order to separate them at intra-beam scattering are estimated. The consequences of the parasitic collision points at multiples of half the bunch the synchrotron radiation are discussed in the conclusions. spacing near the interaction point. Solving (2) for Nf

yields with the usual relativistic factor :

1 INTRODUCTION

Nf = L r =( ) p x (3)

As noticed in the high-ﬁeld option of really large hadron

x y

The choices of at the IP and of the crossing angle colliders (RLHC) [1], the damping time z of the oscilla-

tions in the three degrees of freedom due to the emission are related [5]. Tab. 1 shows the assumed and resulting IP

f s = c =f c

of synchrotron radiation becomes about an hour at a beam parameters. The bunch spacing s ﬁxes by ;

= L N

x y

100 B 12 energy E TeV and a dipole ﬁeld T: is the speed of light. For given and , fol-

lows from (3), and from (2). The beam-beam lifetime

16644 C

= (r =c )( C= )

p tot x

bb is calculated for one interac-

(h)J = z

z (1)

L C 1=E

(TeV )B (T) 2

E tion region, independent of , proportional to and ,

and small for good performance parameters (small x and

x y

Here, z labels the plane ( for horizontal, for vertical be-

= 120

large ); tot mb is the total cross section.The small

s J

tatron oscillations, for synchrotron oscillations), z is the

= y

RMS radii x , compared to LHC [6] or SSC [2], are

damping partition number, C is the circumference and largely due to the higher energy and adiabatic damping.The

2 > R

the bending radius in the arcs of the collider; C=

normalised emittance n has about 1/3 of the SSC value.

includes the long straight insertions for the experiments. p

Scaling their length like E from the SSC [2], and assum-

2 = R + 1708

ing four interaction regions, one gets C= m. Table 1: Interaction region parameters for a 100 TeV p-p

= = 0:003 = = 0:5

y x y

Since the beam lifetime and the duration of a colliding collider with x [6], m,

s =3:75 =60

beam run are usually many hours, the beams have the equi- m, total inelastic cross section inel mb.

9 10

librium beam parameters, given by the equilibrium of quan- Bunch population N= 9.03

tum excitation and synchrotron radiation damping, during Normalised emittance n /nm 367.4

= = y

most of their lifetime. Designing an RLHC such that the RMS beam radius x m 1.313

0 0

= =

beam-beam limit and the desired luminosity are achieved at RMS divergence r 2.626

x y

the equilibrium beam parameters has the advantage that the Luminosity L/(nbs) 30.1

n = L =f inel

emittances of the injected and circulating beams are decou- Events/collision c 22.6 pled, and that the collider is insensitive to slow phenomena Beam-beam lifetime bb /h 42.4 with growth times longer than the damping time.

2 DESIGN PROCEDURE

+ 2.2 Arc Design The design procedure for e e colliders [3] in the DE- SIGN program [4] adjusts the arc and RF system param- The arcs should provide just enough quantum excitation to

eters to achieve a speciﬁed luminosity. Adapting it to p-p achieve the emittance listed in Tab. 1. The average arc ra-

m r R> p

colliders implies setting the mass p , classical radius , dius includes space for the quadrupoles, sextupoles, and Compton wavelength p to their proton values. etc., and short straight sections in the arc cells. In separated

= f = 400

y RF

function FODO cells with x , normalised horizontal frequency MHz, unloaded shunt impedance

Q L Z =60:3 T =2:4

p f

emittance n , arc tune and cell length are related by: G/m and ﬁlling time s, similar to the

LHC values, sufﬁce for the design of the RF system. The

1 RF () R 55 x

p DESIGN program ﬁnds the RF system parameters listed

= L = p

n (4)

2 J Q Q

32 3

in Tab. 4; e and are small. However, the bunch area

4E =c s

e , is comparable to those of LHC and SSC.

()

The correction factor for ﬁnite phase advances F [7]

= ! 0 y tends towards unity for x . The insertions do

not contribute to quantum excitation and momentum com- Table 4: Parameters of the RF system of a 100 TeV p-p col-

= (2R=C )Q

paction . I assume that round beams

= 228:9

lider with circumference C km, harmonic number

with y are achieved by coupling horizontal and ver-

h = 305415 =24 q RF , and quantum lifetime h.

tical betatron oscillations, and apply a factor 1/2 to the tra- V

Voltage RF /MV 35.9

ditional form of (4). Tab. 2 shows the parameters of the

=10

Relative RMS energy spread e 6.53

arcs. The dipole ﬁeld shown [8] is needed in order to ob-

Bucket height/10 22.5

tain colliders in the parameter range I wish to study.

Q =10

Synchrotron tune s 1.27

Bunch length s /mm 27.5

E =c

Table 2: Parameters of the arcs of a 100 TeV p-p collider 4 s

Bunch area e /eVs 0.754

=12 =27:78 R= =1:25 with B T, km and [6]

Arc tune Q 80.62

The time needed for a particle to radiate all its energy,

=2 = =2 y Phase advance x 0.25

and thus also the time needed for acceleration to the oper- L

Cell length p /m 677

ating energy (when synchrotron radiation is neglected) is

Maximum amplitude function x /m 1156

one half of x . If the acceleration time is to be shorter D

Maximum dispersion x /m 8.93

than x , the peak RF voltage must be higher than that

=(2T )

listed in Tab. 4 in the ratio x . The cold vacuum chamber acts as a cryopump. The per- forated beam screen absorbs the synchrotron radiation. Its 3 COLLECTIVE EFFECTS temperature should be much higher than that of the vacuum chamber for good Carnot efﬁciency. Collective effects, in The resistive wall instability, coherent synchrotron tune particular the resistive wall instability (cf. Section 3.1), and shift, longitudinal microwave instability, and transverse the forces during a magnet quench must also be considered. mode coupling instability TMCI are important [10] for the

RLHC [11]. I only study the dominant contribution, and

4E =c = s

2.3 Synchrotron Radiation assume injection at 5 TeV, and a bunch area e

1 I I

eVs there. Below, is the total beam current, and b

Tab. 3 shows several parameters related to the synchrotron Z

is the bunch current. The effective impedances e are

radiation. The total synchrotron radiation power P per

(! ) the weighted sums of Z and the bunch power spec-

beam is three orders of magnitude higher than the 3.6 kW trum [12]. Tab. 5 lists thresholds and growth rates at the

= P=2R in the LHC. The normalised power p is almost energies where they are most critical.The longitudinal mi- two orders of magnitude higher than the 0.2 W in the LHC. crowave and the transverse mode coupling instabilities are

The photon ﬂux , the number of photons per metre of arc below threshold by good factors [13], and not discussed. and per second, is about half the value in LEP2, operating

at 96 GeV and a total current of 14 mA [9]. 3.1 Transverse Resistive Wall Instability

The growth rate of the resistive wall instability is [12]:

Table 3: Synchrotron radiation parameters of a 100 TeV w

U =28

p-p collider with synchrotron radiation loss s MeV

I F r Cc

w p 0 w

=1:5

and horizontal damping time x h. (5)

eZ b (n Q) 0

Beam current I /mA 116

Synchrotron radiation power P /MW 3.24

(n Q)=0:25 n Z

Here, is the tune of the -th mode, 0 is the

Normalised radiation power p/Wm 14.8

impedance of free space, b is the radius of the beam screen,

Critical energy c /keV 12.9

R=Q

and is the average -function. The wall pene-

15 1

=10

Photon ﬂux (sm) 23.3

F = 7:17

tration factor w describes the effects of a beam screen similar to that in the LHC [6], consisting of a thin inner Cu layer and a thicker layer of stainless steel. In the LHC, about half the wall resistivity is caused by the 10 % 2.4 RF System Design

of the circumference with a Cu vacuum chamber at room

e q

The values of s in Tab. 3, and in Tab. 4, and temperature. I ignore this factor in the calculation of the

the parameters of the super-conducting RF cavities, i.e. growth rates. The growth rate in Tab. 5 corresponds w

=1:5

to 147 turns, which can be handled by feedback systems. oscillations s h and for horizontal betatron oscilla-

=3:2

Resistivity and thickness of the inner Cu layer are critical tions x h, obtained with the actual -functions and issues in the design of the beam screen in the LHC [14]. dispersion in the arc cells, are only about twice the corre- If they are both increased by the same factor, the growth sponding synchrotron damping times. The vertical intra- rates and the forces on the screen due to a magnet quench beam scattering time is negative, implying damping, and remain constant. This might open the possibility of reduc- orders of magnitude larger than the other two. In more ing the cryogenic load of the beam screen by operating at tightly focused bunches, IBS may become a limitation [13]. a higher temperature. The resistive power losses due to the image current are much smaller than the synchrotron radi- 4 CONCLUSIONS ation power. An inevitable consequence of designing RLHCs to synchrotron radiation damping times of the order of hours is

Table 5: Growth rates and threshold impedances at the synchrotron radiation power P . When (1) is used to P

100 TeV except where stated otherwise. The beam screen eliminate B , scales as follows:

= 0:03

has a radius b m and consists of two layers. The

3=2 1 1=2

P / E L

x (7) x

inner layer is 50 m of Cu at 5 to 20 K with a resistivity

=1:810

w m, the outer layer is stainless steel.

In the same variables, the stored energy G in one beam is:

1 1

Resistive wall growth rate at 5 TeV /s 8.88

3=2 1=2

=(Z =n) =m

G = E I C =ce = P =2 / E L

Coh. synchrotron tune shift 25.8 =

e x

x (8)

j( Z =n) j =

Long. -wave instability L 0.968

=(Z ) P G

TMCI threshold T /G m at 5 TeV 0.575 Eqs. (7) and (8) demonstrate how and are related by

E L x

x : For a given performance in terms of , , and ,

P G x

and large x , is small and is large, while for small , G

P is large and is small. Numerically, the stored energy in

=8:83 3.2 Coherent Synchrotron Tune Shift one beam is G GJ. This ﬁgure should be compared to 0.33 GJ for the LHC [6], and 0.4 GJ for the SSC [2]. To preserve longitudinal Landau damping, the synchrotron Designing RLHCs such that the synchrotron radiation tune shift must remain smaller than the synchrotron tune damping time is of the order of an hour and that the desired

spread. This leads to an upper limit for the imaginary part

= 0:003

beam-beam tune shift parameter and luminos- 1

of the effective longitudinal impedance [10]:

= 30

ity L (nbs) are reached at the equilibrium beam

parameters leads to interaction region, arc and RF system

Z 6 h V 2

L RF s

RF parameters not too far from extrapolated LHC and SSC pa- =

(6)

n I C b

e rameters. The coherent synchrotron tune shift, driven by the longitudinal broad band impedance of the shielded bel- The coherent synchrotron tune shift is driven by the lon- lows is above threshold by about an order of magnitude, gitudinal broad band impedance that is dominated by the unless one or the other of the measures listed in Section 3.2 shielded bellows [12] in the LHC. Assuming that the beam are taken. The IBS growth times are only a factor of two screen radius and the number of bellows per unit length larger than the synchrotron radiation damping times.

are similar to those in the LHC, the effective longitudi-

=(Z =n) 0:1 nal impedance L is independent of the e 5 REFERENCES machine circumference, and about an order of magnitude

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promising way of increasing the threshold is increasing s [4] DESIGN program written by P.M. Gygi-Hanney.

1=5

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