CHANGE REQUEST NO. ILC-CR-0019

EDMS No:D00000001169785

Created: 12/12/2019

Last modified: 8/1/2020

LUMINOSITY FOR OPERATION AT THE Z-POLE

The luminosity at the center-of-mass energy 91.2 GeV has been estimated based on the accelerator design modified in the Change Request (CR) 16.

RATIONALE

The possible machine operation at the Z-pole (center-of-mass energy 91.2 GeV) was not mentioned in the TDR but has been considered in a few occasions (ref.1, ref.2) in the past. These reports discussed the luminosity scaling with respect to the energy, gave a guess of the luminosity 1-1.5 x 1033 /cm2/s at the Z-pole, based on the luminosity at 250GeV quoted in the TDR, and pointed out several key issues.

Since the positron beam cannot be produced by the undulator scheme using the electron beam of 91.2/2=45.6 GeV, the above reports adopted the so-called ‘5+5Hz operation’, which had already been described in the TDR for the operation below 250 GeV.

In this change request we propose a possible, consistent parameter set at the Z-pole for the first time.

Since the above reports there have been several changes in the accelerator design. They include:

1) The center-of-mass energy has been reduced from 500GeV to 250GeV with shorter linacs (~5km each)

2) The active length of the undulators to produce the positron beam has been extended from 147m to 231m.

3) The normalized horizontal emittance at the IP has been reduced from 10m to 5m by improving the damping emittance from 6m to 4m (CR16). According to this change the luminosity at 250GeV was improved from 0.82 to 1.35 x 1034 /cm2/s.

The major concern on the operation at the Z-pole is that the beam

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energy is so low that the geometric emittance and the relative energy spread are much larger than at 250GeV and that the beam is more fragile against the wake field.

Detailed studies on these issues have been performed by K. Kubo, T. Okugi, and K. Yokoya and the result was published in ref.3.

The Table 1 shows the new parameter set at the Z-pole together with the parameters at 250GeV adopted in CR16.

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Table 1. Accelerator parameters at 91.2 GeV and 250GeV

Center-of-Mass Energy ECM GeV 91.2 250Beam Energy Ebeam GeV 45.6 125Beam collision rate fcol Hz 3.7 5Electron linac repetition rate Hz 3.7+3.7 5Pulse interval in electron main linac ms 135 200Electron energy for e+ production GeV 125 125Number of bunches per pulse nb 1312 1312Bunch population N 1010 2 2Bunch separation tb ns 554 554RMS bunch length at IP z mm 0.41 0.30 Electron RMS Beam energy spread at IP p/p % 0.30 0.188 Positron RMS Beam energy spread at IP p/p % 0.30 0.150 Emittance from DR (x) DR

x m 4 4Emittance from DR (y) DR

y nm 20 20Emittance at main linac exit (x) ML

x m 5 5Emittance at main linac exit (y) ML

y nm 35 30Emittance at IP (x) *

x m 6.2 5Emittance at IP (y) *

y nm 48.5 35Electron polarization P- % 80 80Positron polarization P+ % 30 30Beta_x at IP *

x mm 18 13Beta_y at IP *

y mm 0.39 0.41Beam size at IP (x) *

x m 1.12 0.515 Beam size at IP (y) *

y nm 14.6 7.66 Disruption Parameter (x) Dx 0.41 0.52 Disruption Parameter (y) Dy 31.8 35.0 Geometric luminosity Lgeo 1033 0.95 5.29 Luminosity L 1033 2.05 13.5Luminosity at top 1% % 99.0 74.0 Luminosity enhancement factor HD 2.2 2.55Number of beamstrahlung n 0.841 1.91Beamstrahlung energy loss BS % 0.157 2.62

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SCOPE: ELECTRON MAIN LINAC

There is no change in the machine configuration since CR16, which included the lattice change in the Damping Rings. There must be 5Hz pulsed magnets at the end of the electron main linac but this is in principle already included in the 5+5Hz scenario in the TDR. Depending on the future study results of the undulator radiation from low energy electrons (45.6GeV), a beamline (~ 4-500 meters) for the electron beam might be necessary to bypass the undulator.

VALUE/SCHEDULE IMPACT: VERY SMALL

The bypass line mentioned above may require a small additional cost. Note that this additional beamline runs in parallel with the undulator so that it does not require an extra length of the tunnel. The tuning time of the BDS might be a little longer because finer adjustment of the BDS magnets is needed..

Requested and prepared by:

Kaoru Yokoya

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DETAILED DESCRIPTION OF THE CHANGE REQUEST

Here we give brief discussions on the individual area systems. See ref. 3 for more detailed description.

1. Repetition Rate

The electron beam for the collision at the Z-pole cannot produce positrons by the undulator system. TDR describes the so-called ‘5+5Hz’ operation, in which the electron main linac is operated at 10Hz, half of the pulse (5Hz) is to produce 45.6 GeV beam for collision and the other half is to produce 125GeV beam for positron production. The previous considerations (ref.1 and 2) are based on the 500GeV machine using the full electric power supply system for 500GeV. Now that we have a power system for 250GeV only, the repetition rate must be reduced from 5+5Hz to a smaller number such that the power consumption per meter of the electron main linac does not exceed the value for 250GeV.

We omit here the detailed derivation and give the results in Table. 2. See ref. 3 for the derivation. The possible repetition rate is 3.7+3.7Hz. Hence, we lose a factor 3.7/5=0.74 in the luminosity compared with the previous consideration in ref.1.

Table 2 . The RF system parameters for the alternating operation of 125GeV and 45.6GeV.

e+ production collisionFinal beam energy 125 45.6 GeVAverage accelerating gradient 31.5 8.76 MV/mPeak power per cavity 189 77.2 kWKlystron peak power 9.82 4.15 MWKlystron efficiency 67 53 %Modulator output 14.66 7.83 MWFill time 0.927 0.328 msBeam pulse length 0.727 0.727 msRF pulse length 1.65 1.06 msRepetition rate 3.7 3.7 Hz

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2. The Damping Rings

The damping rings in the TDR are designed for 5+5Hz operation so that they can be operated at the lower rate 3.7+3.7Hz. However, since the lattice design of the rings has been modified in CR16, we have 　 to confirm the performance under the pulse interval 1/3.7Hz/2 = 135ms rather than 1/5Hz = 200ms. It turned out that the required extracted emittance (horizontal and vertical) can be reached by the wiggler field increased by a factor 1.15 (1.48Tesla) compared with the case of the normal 200ms operation. The wiggler design in the TDR can accept this field strength.

The dynamic aperture must also be confirmed under this increased wiggler strength. In this respect there have been some changes since ref. 3.

Firstly, the TDR quotes the requirements on the dynamic aperture such that the ring must accept the positron beam with

Normalized betatron amplitude (Ax+Ay) = 0.07 m.rad Energy deviation = ±0.75%

However, the word ‘betatron amplitude’ is ambiguous and has caused a confusion. It can be the so-called Courant-Snyder invariant defined by

W x=γ x x2+2α x x x

'+β x x'2

(α ,β , γ are the twiss parameters ¿or can be the action variable J x=W x/2. We realized that our positron team has interpreted as Ax=W x whereas our damping ring study has adopted A x=J x. This means that we actually have a wider margin by a factor 2.

Secondly, we had adopted hard-edge dipole magnets in the dynamic aperture study in ref.3 for simplicity. Now we improved the magnet model to a finite length edge. This resulted in a slightly reduced aperture by some 10% level, but this is not serious compared with the factor 2 increase mentioned above.

Figure 1 shows the dynamic aperture of the hard-edge (left) and finite edge (length 0.1m, comparable to the magnet gap) case. The hemi-circle near the origin shows the curve of

(W x+ W y) = 2(J x+ J y) = 0.07m

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Figure 1. The dynamic aperture of the damping ring. For the dipole magnets the hard-edge model (left) and finite edge model of length 10cm (right) are used. The hemi-circle near the origin shows the curve of 2(J x+ J y) = 0.07m. A slight reduction of the dynamic aperture is seen but the aperture is still much larger than the requirement. This new simulation was done by K. Kubo using the computer code SAD.

3. Electron Main LinacThere are several issues to be studied on the Z-pole operation of the

electron main linac. (a) The RF system must deliver different pulses (power and pulse length)

alternatingly with the interval of 135ms.(b)The orbits for the 45.6GeV (colliding) and 125GeV (positron

production) beams are different even without alignment errors due to the earth's curvature. This difference must be corrected before injection to the undulator section.

(c) The emittance increase by the misalignment must be checked. In particular the major concern is the colliding beam because the accelerating gradient is very low.

To obtain 125GeV beam the linac must be operated at full gradient (31.5MV/m). On the other hand, to reach 45.6GeV two different schemes are possible: to operate the first part of the linac at the full gradient and to turn off the rest, or to operate the entire linac at a low gradient (8.76MV/m, see Table 2). In the first scheme the cavities in the unpowered part must be detuned for avoiding the wake field (beam loading) effects. This must be done at 3.7Hz by the piezo tuner, which is already equipped for compensating the Lorentz detuning, but the dynamic

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range of the tuner is far from sufficient for this purpose of the detuning. Thus, we must adopt the second scheme, i.e., uniform, low gradient operation. There seems to be no other RF-technical problem in (a).

For the issue (b) a simulation showed that the orbit difference at the exit of the main linac amounts to ~10mm. This can be corrected by using pulsed magnets at 3.7Hz. The beamline for this end has not yet been designed but no serious problem is expected. In this respect there is one more issue to be studied. These pulsed magnets lead both the 45.6GeV beam and 125GeV beam to the center of the undulators. The radiation from the 45.6GeV is not used for positron production but the radiation angle (proportional to 1/) is much larger than that from the 125GeV beam. Most of the radiation is stopped by the masks inserted between the undulators but some fraction would hit the inner surface of the superconducting wiggler. The amount of such radiation has not yet been estimated. In the case it turns out to be too strong, we need to prepare an electron beamline for the 45.6GeV beam to bypass the undulators.

For the issue (c) simulations have been done under the following assumptions.

The orbit correction was done for the colliding beam. (The emittance increase of the positron production beam is not an issue.)

The following random alignments are assumed (the numbers are r.m.s., cut at 3 sigmas): Quadrupole offset 0.36mm Cavity offset 0.67mm, tilt 0.3mm BPM offset 1m

Initial normalized emittance y = 20nm DFS (Dispersion-free steering) with energy change 20%.

Two cases were simulated for the bunch length and the initial energy spread:

Bunch length 0.3mm, energy spread at the linac end 1.2% Bunch length 0.41mm, energy spread at the linac end 0.9%

The reason of the second case is explained in the next section.Figure 2 shows the vertical emittance increase in the misaligned linac as a function of the final beam energy. Two cases of different bunch length are shown.

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Figure 2. The average vertical emittance increase in the main linac as a function of the final beam energy (same linac length). The error bars indicate one standard deviation in 100 runs with different random number seeds.

The average emittance increase of the 45.6GeV beam in the main linac with z =0.41mm is 6.3nm. TDR quotes 5.3nm as the average emittance increase at upstream of the bunch compressor and additional 1.1nm in the bunch compressor. Adding all these numbers on top of the damping ring emittance 20nm, we find the average vertical emittance at the main linac end to be y ~ 33nm. We adopted 35nm as the vertical emittance at the linac end in Table 1.

4. Beam Delivery System (BDS)

There are three major issues in BDS related to the Z-pole operation. All of them come from the low beam energy.

Collimation depth Momentum band width Wake field effects

(A) Collimation depthThe horizontal beam angle spread (r.m.s.) at the interaction point (IP) is given by

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θx¿=√ ε x, nγ βx

¿

where ε x ,n is the normalized horizontal emittance and βx¿ is the horizontal

beta function at the IP. This angle becomes large as the beam energy becomes lower. The synchrotron radiation from the beam halo will have a very large angle and may hit the final quadrupole magnets, causing backgrounds to the experiment. In such cases the beam halo is usually scraped out in upstream collimators. However, with the TDR parameter βx

¿=13mm∧ε x ,n=10μm, the beam must be collimated at ~6σ x, which is already marginal, at the beam energy 125GeV. Hence, to keep the collimation depth > 6σ x at 45.6GeV, the horizontal beta function must be as large as βx

¿ = 13mm ׿125GeV/45.6GeV) ׿5μm /10μm) = 18mm, where 5 μm is the horizontal emittance in the present design.

(B) Momentum band width

The relative beam energy spread σ EE at the IP is proportional to 1/Eσ z .It is

~0.15% at ECM=250GeV. If the bunch length (0.3mm) is fixed, the energy spread for Z-pole operation is ~0.41%. This large (relative) energy spread may cause an emittance growth in the BDS due to the chromatic effects. It turned out by a simulation this emittance growth is too large. We decided to adopt the bunch length 0.41mm (rather than the standard value 0.3mm) so that the relative energy spread at the IP is reduced to 0.3%. This is done by tweaking the parameters of the bunch compressor (no problem is expected). This longer bunch has a few side effects: The transverse wake field in the linac increases by a factor ~0.41/0.3. The transverse wake field in the BDS increases by the same factor. The disruption parameter at the IP increases by the same factorThe first one was mentioned in the previous section. The second one will be discussed in the next subsection, and the third one in the section of the beam-beam interaction.

(C) Wake field effectsIncluding all the effects (increased bunch length, wake field, magnet/BPM misalignment, assumed beta functions, etc.) intensive simulations of the BDS tuning process have been done. Table 3 shows the magnet errors used in the simulations.

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Table 3. Magnet errors used in the simulation of BDS

Bend rotation 100 radfield strength / 1x10-4 bend-to-BPM alignment 100 m

Quad alignment (x,y) 100 mrotation 100 radfield strength K1/K1 1x10-4

sextupole component (B2/B1 at r=1cm) 1x10-4

Quad-to-BPM alignment 5 mSext alignment (x,y) 100 m

rotation 100 radfield strength K2/K2 1x10-4

sext-to-BPM alignment 5 m

Figure 3. Evolution of the vertical beam size during the process of tuning. The horizontal axis is the integrated number of knobs. The average of 100 different random number seeds is shown. Two different values (5m and 10m) are used as the r.m.s. misalignment of the BPMs with respect to the center of the quadrupole and sextupole magnets.

Figure 3 shows the vertical beam size during the process of tuning in the absence of wake fields. Two cases of different errors of the distance from the BPM center to the quadrupole/sextupole magnet center (5m and

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10m in r.m.s.) are shown. 10m is the value used in the BDS simulations of ILC in the past. We expect an improvement to ~5m during a few years of operation experience will be possible. Table 3 shows the horizontal and vertical beam sizes obtained in the simulations of various cases. For the wake field effects the offset 300m of the wake sources is used. 5m is used as the BPM misalignment w.r.t. the quadrupole/sextupole magnets. We adopted these beam sizes (1.12m and 14.6nm), converted to the equivalent emittances, in the parameter table (Table 1).

Table 3. Simulation results of the beam sizes. The offset of 300m of the wake field sources is used for the row (3) and (4).

x* (m) y* (m)No errors 1.04 12.7Magnet errors and correction 1.12 14.0Magnet errors + static wake fields + correction 14.3Magnet errors + static/dynamic wake + correction

14.6

These simulations show that the following issues are important for the BDS tuning especially at the Z-pole. Accurate alignment between the magnet field centers and the electric

center of BPMs. Sufficient RF contact for the bellows and flange gaps to minimize the

wakes. Relaxing the intensity dependence due to the static wake effects by

wake field knobs.

5 Beam-Beam Interaction

The luminosity calculated by CAIN from the parameters in Table 1 is ~2.05×1033 /cm2/s, which is a little higher than the value expected in ref.1 in spite of the reduced repetition rate, owing to the reduced horizontal emittance in CR16. Figure 4 shows the luminosity spectrum. The dashed curve shows the initial distribution normalized at the peak. As is seen, the contribution of the beamtrahlung is very small.

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Because of the longer bunch to reduce the energy spread, the vertical disruption parameter is slightly enlarged (Dy=31.8). Nonetheless, it is still lower than the value 34.5 for ECM=250GeV case. Therefore, the tolerance of the beam offset will not be severer (~0.1y*).

Figure 4. Luminosity spectrum. The red dashed curve shows the initial distribution normalized at the peak.

6 Luminosity UpgradeWe do not foresee a major obstacle in doubling the luminosity by

doubling the number of bunches from 1312 to 2625. Once the RF system is reinforced for the doubled bunches, we expect to reach L~ 4×1033/cm2/s at the Z-pole.

REFERENCES1 N. Walker, “ILC possibilities at Z and W”,

http://ilcdoc.linearcollider.org/record/63004?ln=ja

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2 K. Yokoya, “Z-pole Operation”, LCWS2016 at Morioka, https://agenda.linearcollider.org/event/7371/contributions/38173/

3 K. Yokoya, K. Kubo and T. Okugi, “Operation of ILC250 at the Z-pole”, http://arxiv.org/abs/1908.08212

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Version: modified: by: what:1 12.12.2019 KY Initial version1.1 8.1.2020 BL formatting

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