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� �� Nobukazu Toge (KEK)

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Flux concentrator in construction / testing

34

Positron Source• Flux Concentrator (FC) is a device which is used as OMD (Optical Matching Device)

in a positron production system. FC can produce strongly focused ~solenoid field (6-10T) out of eddy current that is induced by pulsed primary coil current on its outside. However, FC, generally is limited in its pulse length (< 30 µs).

• Other devices to use as OMD include: – AMD (adiabatic matching device) – a solenoid magnet with adiabatically changing field

strength; – QWT (quarter-wavelength transformer) – a short strong solenoid followed by a weaker

solenoid; – LL (Lithium lens).

They can replace FC for longer pulses but at lower magnetic field, or require additional R&D.

T.Kamitani

36

Positron production system at the KEK electron/positron injector linac.

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37H.Oguri et al

• Electrons can be stripped off H- easily when an accelerated H- passes through thin foils immediately after injection in RCS.

• Radiation effect on and lifetime of the charge-conversion foils have to be dealt with, however. 38

H- to inject

Proton in RCS

Advantage of H- for Injection into RCS (Rapid Cycling Synchrotron)

Foil

Dipole magnets

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39

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B = 0.2528 Tp = 7GeV/cL = 5.804m

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r = 92.37m

41

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Q2’8 !.&360���#-560/�-%+(��'����)��?26182 x p / 0.0628 = ?

Dipole MagnetsQ6: LHC now has beam momentum 3.5 TeV. Ring circumference is 27km. What is the required B, if the whole ring is completed packed by dipole magnets?

A6:

• r = C / 2p= 27000 / (2 x 3.14) = 4297.2 m

• Remember, 3.3356p = Br• B = 3.3356p / r

= 3.3356 x 3.5e3 / 4297.2 = 2.72T

Q7: The LHC dipoles are actually running at ~4.2T for 3.5TeV beam. What is the “dipole packing factor?”

A7:

• Remember, 3.3356p = Br• Bending radius in dipoles with B = 4.2T

would be r = 3.3356p / B

= 3.3356 x 3.5e3 / 4.2 = 2779.7 m

• Total length to occupy with dipoles would be

2 p r = 2 x 3.14 x 2779.7 = 17.465 km

• Packing factor = 17.5e3 / 27e3 = 65%

(Actually LHC has 1232 units of dipoles, each 15m long) 42

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43

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44

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Single-Particle Optics• We saw that a thin quad magnet (GL) acts like

a focusing / defocusing lens with F = 3.3356p/(GL).

What if you had a series of such magnets spaced apart by L ?

(NB: That L is different from that within (GL); sorry about the confusing notation.)

• Let us characterize the particle trajectory in x with a “vector”

(x, x’). x is the location of the particle and x’ is the angle of the trajectory, i.e.

x’ = dx / dswhere s denotes the coordinate along the canonical trajectory.

In the following discussion, we ignore particle acceleration for simplicity.

• One sees that if there are no magnetic components along the beamline, after a length of s, the (x, x’) of the particle would be like,

x(s) = x(0) + s x’(0)x’(s) = x’(0)

So in vector notation,

• What is the effect of a thin quad (e.g. ignore the thickness) with focal length F on (x, x’)?The quad does not change x, but does change x’ by x’ à x’ – x/F

We call matrices like these “beam transfer matrices”.

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Single-Particle Optics• What if we had an N series of such

“cells”? à It is equivalent to considering MN. This issue is considered more transparently if we ask help of engenvalues / vectors.

48

• Consider a system that consists of a drift L (*not to mix with quad thickness!), a thin defoc quad (-F), another drift L, a foc thin quad (F). What is this system’s beam transfer matrix M?

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Single-Particle Optics• So, if

(Tr M / 2)2 < 1-1 < 1 – L2/2F2 < 1, i.e.| L / 2F | < 1

Then the eigenvalues will be complex. Since l1 l2 = 1, they can be written as

l1 = e –iµ, l2 = e +iµ

and MN will not be divergent!

à Principle of FoDo lattice.

Q9: We have magnets with G = 1T/m, thickness 0.5m. Let us set the half cell length of FoDo to be 5m (full length 10m). For which momentum range can this beamline act as a non-divergent FoDo?

Q10: How would all the analysis above change, if we do NOT ignore the thickness of the quads?

49

• So the question reduces to evaluating the eigenvalues of M. Recall the basic linear algebra.

Note: det M = 1, because all the transfer matrices of the “components” which contributed to M have their determinant 1.

divergent. is real, is if Hence,

1

so

.1 where,

0

Thus,

0 of solutions are , sEigenvalue

21

21

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FoDo Lattice Examples

50

Beamline of ATF2

ATF damping ring

• Iron saturates at ~ 2T. This gives limitation to the field strength achievable with normal-conducting iron-dominated (NC) magnets. For instance, dipole magnets with B > 1.5 T, or quadrupole magnets with a G > 1T (a is the “aperture” of the quad) should go “superconducting” (SC).

• SC magnets, without iron, can produce higher field. But, because of the absence of the iron poles, one has to carefully arrange the electric current distribution to produce the desired field pattern. à Lecture by Tsuchiya

• SC magnets, with iron, is, again, limited in strength, similarly to NC magnets. However, they are substantially lower power consuming.

Superconducting Magnets

QCS for SuperKEKB

52

Magnets - Comments• Generally, Maxwell’s equation allows solutions of

many higher order fields besides dipole and quadrupole fields (sextupole, octapole, decapole, dodecapole etc).

• Such fields are sometimes useful for beam controls; They are also sometimes very harmful.

• It is important to control the higher pole field. This leads to tolerance issues of the magnetic poles (NC) or current distribution (SC).

• Thermal effects and mechanical aspects are also important issues for practical magnet designs and operation.

• Survey and alignment of the magnets are critical tasks to do before starting operation of a new accelerator.

• Finally, magnet power supplies (settability, stability and lifetime) are a very important area which is sometimes overlooked.

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66

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• ���?W`Z�#5J=,-GI'$�%W`ZL��5J2=L��=5J[^R�#�L) �[^R*=�-�F+J(W`ZOV\P`B���ACC?4;OV\P`��B36>,a��815Jb[^R�#�F+J(

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SuperKEKB No Yes YesJ-PARC MR Yes No No

LHC MR Yes Yes Yes

67

Livingston Chart

By Stanley Livingston (1954)

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Created by: Takuya Natsui(KEK)

Created by Takuya Natsui,for KEK open day display

Created by: Takuya Natsui(KEK)

Created by Takuya Natsui,for KEK open day display

Standing Wave Accelerator Structure (p/2)

Created by Takuya Natsui,for KEK open day display

.2/����)�(�����)

73

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,1��+.2/� ��$*��'���)RF� )1/2+��#%*"'&�����&.2/�+���(��$*"' &!*�

•Q1: fRF = 1.3GHz )'!� p-02-)��),1�#4

•A1: f = 1.3�109 Hz; c = 2.9979�108 m/sà l = c/f = 0.23 m; p-02-)��,1� = l/2 = 0.12 m

9-,1��)�

�#��+/15:6��,�!• �38 “pillbox” ��: Maxwell ���2 ')$����* - –

• ((+,– c01 = 2.4048

– w010 = c01 c / b

• (, ,()2%pillbox ��,TM01 7:4 &(��7:4, /0��+-TM010 7:4<)..

74

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RF Frequencies

• L band 1 - 2 GHz• S band 2 - 4 GHz• C band 4 - 8 GHz• X band 8 - 12 GHz• K band 12 - 40 GHz

• Q band 30 - 50 GHz

• U band 40 - 60 GHz

• V band 50 - 75 GHz

• E band 60 - 90 GHz

• W band 75 - 110GHz

• F band 90 - 140 GHz

• D band 110 - 170 GHz

76

The naming of frequency ranges on the left came apparently from the convention which was developed in Rader-related research effort in Allied countries during WWII.

Other than that, no one seems to know for sure why this pattern, except perhaps L stands for LONG and S stands for SHORT.

Resonant Cavities• Quality factor (Q-value) of a cavity:

– [stored energy in the cavity] / [energy loss over 1rad of RF oscillation]

• In case of a TM01 mode, the stored energy in a pillbox cavity is

• Surface current in the cavity is

• Ohmic energy loss is surface integral of rsJ2/2 -

77

25.021~)(

21

21 2

000121

200

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ø

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Resonant Cavities• From the previous page, the Q value that we seek is given by

• In case of copper Q ~ 5000, in case of superconducting Nb Q ~ 1010

78

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öççè

æ+

=D

=

2201

001

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s cr

µcw

Resonant Cavities

• Shunt impedance Rs of an accelerator cavity is defined as

Rs = (Energy gain V0 by a particle across the cavity)2 / DP

• For a pillbox cavity the Rs is given by

• Where “T” is the transient factor.

• In case of copper: Rs = 15-50MW/m for 200MHz, 100MW/m for 3GHz 79

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)(11

1

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www

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pr

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QRs

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20=

Geometric quantity of a cavity.

Superconducting Cavity at superKEKB

80

81

Accelerator Resonant Cavity (Single-cell superconducting)

This is an example of a single-cell super-conducting cavity which wasused at KEKB.

Accelerator Cavities / Structures• Q2: If fRF = 1.3GHz for a p-mode cavity, what should be the cell length? • A2:

f = 1.3E9 Hz; c = 2.9979E8 m/sà l = c/f = 0.23 m; p-mode cell length = l/2 = 0.12 m

• Q3: If fRF = 2.856GHz for a 2p/3-mode structure, what should be the cell length?

• A3:f = 2.856E9 Hz; c = 2.9979E8 m/sà l = c/f = 0.105 m;

2p/3-mode cell length = (2/3)l/2 = 0.035m

82

Accelerator Cavity / Structure -Comments

• Cavities have many resonant modes. TM01 is the lowest and is most often used for beam acceleration. But,

– Higher-order modes, such as TE11, also can be excited with an external RF source,

– Or by the beam that traverses through them off axis,– And do some harms. This may not be big problems for

many applications, but it is for some.

83

TE11 mode (~1.5 x TM01)

T.Higo, et al

Accelerator Resonant Cavity (Single-cell normal conducting)

84

This is an example of a single-cell normal conducting cavity (which is used at superKEKB. It has “slots” for removing (damping) HOM, as excited by the beam, which are harmful for multi-bunch beam operation, and an energy storage cavity to reduce the effects of beam loading on the system.

T.Abe

Accelerator Cavity / Structure -

Comments• Design, engineering and operation of

accelerator cavities / structures is a huge

area.– Exact evaluation of resonant frequencies, shunt

impedance and quality factor have to be made

through numerical calculations (still, an intuitive

understanding important).

– Size variation à variation of resonance frequencies

à mechanical tolerance and tuning issues. Similarly,

temperature stabilization issues. (Q: if DT = 5deg,

how much energy shift for an X-band structure?)

– “Couplers” to let the external RF power into the

cavities and vice versa.

– In pulsed mode operation, the accelerator cavities

exhibit transient behaviors at the beginning and end

of RF pulses.

– Even in continuous wave operation, the accelerator

cavities see transient effects when the beams pass

through them.

85E.Kako, S.Noguchi et al

Microwave (RF) Source(Klystrons)

• For brevity, the solenoid beam focusing magnet is omitted from the illustration above.• Klystron, in a way, is a reversed accelerator, which extracts RF power from the beam.• Klystrons, depending on the type, operate in pulsed- or continual modes.

86

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city

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mod

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Microwave (RF) Source(Klystrons)

87J-PARC

Microwave (RF) Source(Modulator + Klystrons)

88Klystrons for pulsed operation

rModulator

T.Okugi

A typical electron linac

89

Surface level (Klystron Gallery)

Underground tunnel

KlystronModulatorDC PS

Waveguides

Accelerator structures(2m x 4)

Control equip/

Beam focusingmagnets

90

Microwave (RF) Source(Modulator + Klystrons)

Tsukuba injector linac

91

Microwave RF Source (Klystrons) -Comments

• As said in the previous page, klystrons are like small-scale reversed accelerator, and are more difficult ones at that.

– Relatively low beam energy (up to few hundred kV).– High current (tens of A)– So large beam power, and large space-charge effect.– Large beam size.– Opportunities for a good number of resonant behaviors, besides the RF power that you

intend to produce.

• Design, engineering and operation of klystrons is a huge area, too, in a way similar to those for accelerator cavities / structures.

– RF calculations and simulations, under prominent effect of space-charge force.– Tolerance and tuning issues.– RF windows to isolate the klystron vacuum and outside vacuum. Sometimes a cause of

trouble à another large area of studies which I cannot detail.– Cathode lifetime. Klystrons are a consumable component. Significantly more so than

accelerator cavities / structures.92

Manipulation of RF Power• RF pulse compression with SLED is often used for linac RF source.

• Power higher than what is available from a klystron, although the effective pulse length becomes shorter.

• Many NC electron linacs use SLED (but not all). 93

RF voltage at the hybrid output, ignoring the power coming out of SLED.RF voltage of the power coming out of SLED.

RF voltage of the power, combined from the klystron and the one coming out of SLED.

RF voltage of the power, as it is induced within the accelerator structure.

SLED cavity at injector linac of KEK (Tsukuba)

94

The Beam• How does one characterize the transverse

spread of the beam, i.e. that of a group of many particles?

– Consider an ensemble of particles with distributed (x, px), measured from the beam centroid.

– Take (x, px) as the canonically conjugate variables of motion, and take it that they consitute the “Phase Space” of the group of particles.

– If acceleration is ignored, (x, x’) can serve the purpose instead of (x, px).

– Same goes for (y, py) and (z, E).

• So, take the area occupied by particles in the (x, x’) plane (it is a virtual plane) , and call it - “Beam Emittance in x”.

– Dimension of transverse beam emittance is, thus, (m),

95

• Systematic analysis of all these in practical beamlines requires much elaboration of single-particle motions, starting from the previous pages. My lecture cannot really cover this critical topic at all! Trust that Ohmi san’s lecture covers it in detail.

Synchrotron Radiation

96

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Rate of energy loss due to SR

Energy loss per revolution per particle

(m)(GeV)

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Q11: A 3km ring is using dipole magnets with r = 90m and is storing 3A of 8GeV electrons. What is the “average total” power to compensate the SR energy loss, per unit time?

�����

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Beam Monitors• Cavity Type Beam Position Monitors (BPM): Rather than seeing induced charges on

electrodes, measure the transverse modes (TE-modes) that are induced by the beam when it passes off center of a cavity.

KEK-Pohan-SLAC Collaboration

Beam Monitors• Beam Current Monitors: BPMs can

also measure the beam intensity but for better precision a dedicated beam current monitor is used, as shown on the right.

• Beam Profile Monitors with phospho-screens:

– Direct measurement of the beam, in case of linac or beamlines.

– Measurement of synchrotron radiation light in case of rings (on the right).

R\U+�• 1[LWOMVP2AFHR\UTZSKLXB �

– R\UJ��HF5A-�[LWJ"�]D<C/-�[LWJ��HF5AR\U�'J�H^

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– (��BR\UQXO6�)03H#�BR\U�'���6)�?@H0

– -�[LW>@8/%4Y\N&J�5��E3G0

H.Hayano et al

Beam Monitors• Beam Profile Measurement with

interference method of SR light in rings.

– Take advantage of the interference of SR light which comes through a slit pair.

– Overcomes the diffraction limit in standard SR measurement.

a = beam size; g = “visibility” (clearness)l = wavelength; D = slit separationL0 = distance from the light emission point

T.Mitsuhashi and T.Naito

Beam Monitors

• Beam size monitor with Compton scattering off interfering pattern of laser photon population.

• Data on left (2010/5) at ATF2:– Laser WL: 532 nm– Laser crossing: 3 deg– Fringe pitch: 3.81 µm– Modulation: 0.87– Beam size: 310 +/- 30 nm

T.Tauchi

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Controls• Controls systems at particle

accelerators must allow you to– Monitor– Analyze– Compute / Simulate– Control– Log

• A wide range of synchronous and asynchronous signal processing / transmission must be managed.

• Nearly a unique hotline to speak to the hardware, once the tunnel is closed for operation.

Schematic diagram of KEKB control system (N.Yamamoto)

Controls• Controls systems at particle

accelerators must allow you to– Monitor– Analyze– Compute / Simulate– Control– Log

• A wide range of synchronous and asynchronous signal processing / transmission must be managed.

• Nearly a unique hotline to speak to the hardware, once the tunnel is closed for operation.

Schematic diagram of KEKB control system (N.Yamamoto)T.Okugi

Controls• Controls systems at particle

accelerators must allow you to– Monitor– Analyze– Compute / Simulate– Control– Log

• A wide range of synchronous and asynchronous signal processing / transmission must be managed.

• Nearly a unique hotline to speak to the hardware, once the tunnel is closed for operation.

Schematic diagram of KEKB control system (N.Yamamoto)

N.Yamamoto

Controls• Controls systems at particle

accelerators must allow you to– Monitor– Analyze– Compute / Simulate– Control– Log

• A wide range of synchronous and asynchronous signal processing / transmission must be managed.

• Nearly a unique hotline to speak to the hardware, once the tunnel is closed for operation.

Schematic diagram of KEKB control system (N.Yamamoto)

N.Yamamoto

Conventional Facilities

KEK

Conventional Facilities• Sometimes the tunnel length becomes too

big to stay inside a lab campus.– Going underground.– Going off site.– Safety issues.

• At any rate, you have to – Fit all required beamline components in

wherever they have to go.– Connect them all either electronically,

mechanically and vacuum-wise.– Allow enough space for installation and

maintenance activities, plus, survey and alignment sighting.

– Bring in fresh air and provide adequate cooling (taking the heat the out).

– Ensure safety for personnel and equipment.

EuroXFEL in Hamburg

LHC from satellite

Conventional Facilitiesf5200 mm

645 mm

EuroXFEL in Hamburg

112

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• �4I&�QTRJ6�8HFDEMDE�?9>F6�?=G9>FI��P*:U*DE?K:V7

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–5$�63�� 6��S � 6����65���…

��• ��'�,�!����-+"%�(�% ,%�'!*&���#��� ��-��$��) 6

– �.24/5���0315 OHO (��). online ����→ http://accwww2.kek.jp/oho/OHOtxt4.html

– S.Y.Lee: Accelerator Physics, World Scientific, 2004. → https://books.google.co.jp/books?id=VTc8Sdld5S8C&printsec=frontcover&dq=accelerator+physics+lee&hl=ja&ei=31bOTPOYJ42lcbac7dMO&sa=X&oi=book_result&ct=result#v=onepage&q&f=false

– D.Edwards and M.Syphers: AIP Conf. Proc. 184, 1989, American Institute of Physics → http://scitation.aip.org/content/aip/proceeding/aipcp/10.1063/1.38066;jsessionid=xlEo7HyrcW4jjcXLvsYaGQg8.x-aip-live-03

– H.Wiedemann: Particle Accelerator Physics, Springer Verlag, 1993. → http://ph381.edu.physics.uoc.gr/Particle_Accelerator_Physics.pdf

115

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