Chapter 4. Booster Synchrotron

Chapter 4. Booster synchrotron

Contents

Chapter 4. Booster synchrotron...... 59 4.1. General parameters of the Booster...... 60 4.2. Lattice & beam dynamics...... 62 4.3. BOOSTER magnets...... 63 4.3.1. Normal conducting magnetic system...... 64 4.3.2. Superconducting magnetic system...... 65 4.3.2.1. Dipole Magnet...... 66 4.3.2.2. Quadrupole Lens...... 69 4.4. Injection and extraction...... 69 4.5. Collimation...... 71 4.6. Beam acceleration. RF system...... 73 4.6.1. Adiabatic trapping...... 73 4.6.2. First stage of acceleration...... 75 4.6.3. Beam bunching at 1st harmonics and electron cooling...... 76 4.6.4. Second stage of acceleration...... 76 4.6.5. Acceleration system...... 77 4.7. Tune shift at injection and at extraction...... 78 4.8. Emittance growth after crossing the stripping foil...... 79 4.9. Electron cooling system...... 80 4.9.1. Ion energy choice for electron cooling application...... 80 4.9.2. Recombination in the cooler section...... 82 4.9.3. Design of the Booster electron cooler...... 84 4.9.4. Stabilization of the ion beam emittance with electron cooling...... 85 4.9.5. Simulation of cooling process with BETACOOL...... 87 4.10. Schedule of the works. Estimated cost...... 89 4.11. References...... 89

59 4.1. General parameters of the Booster

The main functions of the intermediate heavy ion synchrotron, the Booster of the Nuclotron, are the following:  Accumulation of 4∙109 U32+ ions in the Booster;  Acceleration of the ions up to energy of 400 MeV/u that is sufficient for stripping of the Uranium ions up to the charge state of 92+;  Simplification of the requirements to the vacuum conditions in the Nuclotron owing to higher energy and charge state of the ions injected into the Nuclotron;  Decrease of the ion beam longitudinal emittance at the energy of 100 MeV/u approximately by application of the electron cooling.

The present layout of the Nuclotron and existing injection and extraction systems make it possible to place the Booster having 216 m circumference and four fold symmetry inside of the Synchrophasotron yoke (see Fig. 4.1.1 and 4.1.2).

Four large straight sections will be used for injection from the linac, one turn extraction to transfer the beams into the Nuclotron, placing of the acceleration cavity and electron cooler (Fig. 4.1.3).

Figure 4.1.1. Fragment of the Figure 4.1.2. Booster position inside of the Synchrophasotron iron yoke. Synchrophasotron yoke (cross section).

We considered two versions of the Booster lattice - DFO and FODO periodicity. DFO lattice provides more efficient collimation of charge exchanged ions whereas the FODO one has other well-known advantages. Low initial intensity level (about 4∙109 particles per pulse) allows us to install small number of collimators to clean out the U33+ ions from the U32+ beam. That is why the FODO lattice is considered as more preferable for further consideration. Main Booster parameters are listed in the Table 4.1.1. The Booster cycle diagram is shown in the Fig. 4.1.4.

60 The Booster Ring

The Electron Cooler

Figure 4.1.3. Booster location in the Synchrophasotron yoke

Table 4.1.1. Basic Booster parameters. Ions U32+ Circumference, m 216 m Fold symmetry 4 Quadrupole periodicity 24 Injection/extraction energy U32+, MeV/u 6.2/400 Magnetic rigidity, T·m 2.4  25.0 Dipole field, T 0.17  1.5 Pulse repetition rate, Hz 0.25 Magnetic field ramp, T/s 1.5 Beam Injection type twice repeated single turn Beam extraction type Single turn Injection store duration, sec 0.8 Vacuum, Torr 10-11 U32+ beam intensity, ions per pulse 6×1010 Transition energy, GeV/u 3.9

Figure 4.1.4. Booster cycle diagram

61 4.2. Lattice & beam dynamics

The chosen lattice (Table 4.2.1 and Fig. 4.2.1, 4.2.2) contains 4 arcs. Each arc consists of 5 regular FODO cells with dipoles and one without them. One regular cell includes focusing and defocusing quadrupoles, one sector dipole and small drift section used for location of magnetic correctors, beam position monitors, collimators and so on. The equipment of injection, ejection and acceleration are placed in the four large straight sections. The possible position of the working point for this lattice version is given in the resonance diagram 4.2.1. There are only two systematic betatron difference resonances of the forth order: 3Qx – Qy =12 and 3Qy – Qx =12. Both are quite distant from the working point Qx,y ≈ 5.8.

Table 4.2.1. Lattice parameters of the Booster. Fold symmetry 4 Number of the FODO lattice cells per arc 6 Length of lattice cell, m 9.0 Length of large straight sections per cell, m 4.1×2 Length of small straight sections, m 0.65 Betatron tunes 5.8/5.85 Phase advance per cell 1.51 Amplitude of β-functions, m 17.0 Maximum dispersion function, m 2.9 Momentum compaction factor 0.038 Chromaticity -7.0 Horizontal acceptance, π∙mm∙mrad 400 Vertical acceptance, π∙mm∙mrad 70

Figure 4.2.1. Betatron resonances in vicinity of the working point.

62 Figure 4.2.2. Betatron and dispersion functions for one FODO arc.

4.3. BOOSTER magnets

The magnetic system of the booster consists of 4 quadrants. There are 10 dipole magnets, 6 focusing and 6 defocusing lenses in each one. The multipole correctors are also used to compensate the errors of both main (dipole, quadrupole) and higher (sextupole, octupole) harmonics of the magnetic field. The needed magnetic field induction in aperture is 1.5 T at maximum rigidity (Table 4.3.1). The large aperture of both lattice dipole and quadrupole magnets is one of the main design features.

Table 4.3.1. Lattice magnets. Dipoles Number of dipoles 40 Maximum magnetic field, T 1.51 Effective field length, m 2.6 Bending angle, deg 9.0 Curvature radius , m 16.55 Vacuum chamber, mm2 150 x 62 Quadrupoles Number of quadrupoles 48 Field gradient, T/m 20 Effective field length, m 0.4 Vacuum chamber aperture, mm2 150 x 62

The requirements for dipole and quadrupole magnets of the Booster can be met using either – normal conducting or superconducting windings. In this report we consider the normal conducting version of the magnets as a base line for the Booster design. The Nuclotron-type magnets are discussed as a reserve option.

63 4.3.1. Normal conducting magnetic system

The normal conducting booster was designed for the fist project of the heavy ion accelerator complex at the JINR [4.3.1]. As an example the quadrupole lens design is presented in the Fig. 4.3.1.1.

Figure 4.3.1.1. Drawing of the quadrupole lens designed for heavy ion booster in [4.3.1].

Other close prototypes of the Booster magnets are the magnets used in IHEP and ITEP boosters.

Presently technical design of the Booster magnets is in progress. Preliminary drawings of the dipole magnet are shown in the Fig. 4.3.1.2 and its parameters are listed in the Table 4.3.1.1. Total electric power required for supply the Booster magnetic system is less than 3 MW.

Fabrication of the Booster magnetic system can be performed in the JINR machinery workshop. Estimated cast of one dipole magnet is about 30 k$.

64 Figure 4.3.1.2. Preliminary design of the Booster dipole magnet.

Table 4.3.1.1. Parameters of the Booster dipole magnets. Weight, kg 2915 Iron yoke а) dimensions, mm 400*730*1300 b) weight, kg 2610 Winding а) weight, kg 310 b) length, m 130 c) dimensions of the cupper pipe, mm 18.5*18.5*9.5 d) number of turns 16*2=32

Resistance, Ohm 0.00849 Inductivity, mH 6.75 Current at 1.6 Т, A 3312.5 Mean current, A 1657 А

4.3.2. Superconducting magnetic system

The magnetic system based on superconducting magnets is considered as an alternative. The Nuclotron-type design based on a window-frame iron yoke and a single - layer saddle-shaped

65 superconductor winding can be chosen for the Booster [4.3.2]. Nevertheless, a further development of the technology was proposed [4.3.3] to increase the efficiency of the magnetic system. In accordance with this proposal the cold mass of the magnet, consisting of a SC- winding, a beam pipe, a reinforcing shell and correcting windings (if needed) are fabricated as a common rigid unit separated from the iron yoke. The last one is kept at a temperature of 80 K. A small vacuum gap between the outer surface of the cold mass at 4.7 K and the internal surface of the yoke is used to avoid a direct heat infiltration from the iron to the SC-winding. The cold mass having a substantially lower weight and surface and the cooled iron yoke are suspended inside the cryostat, for example, by suspension parts similar to those used at the Nuclotron. The main characteristics of the magnetic system are given in Table 4.3.2.1.

Table 4.3.2.1. Main Characteristics of the Magnetic System. Circumference 216 m Max magnetic rigidity 27 Tm Feld ramp 1.5 T/s DIPOLE MAGNETS Maximum magnetic field 1.5 T Number 40 Effective length 2*1.3 m Aperture 160 mm x 70 mm Mass 1500 kg QUADRUPOLE LENSES Maximum gradient 20 T/m Number of quadrupole 24 Effective length 400 mm Mass 220 kg

4.3.2.1. Dipole Magnet

Main dynamic forces in the magnet winding are compensated by the bandage of glassfiber tape and synthetic thread (see Fig. 4.3.2.1). Dynamic forces due to a non-symmetrical position of the cold mass in the magnetic gap are compensated by 76 horizontal and 26 vertical thermal insulating spacers. The magnet is of demountable construction. The yoke consists of two symmetrical parts connected to each other by means of bolts. The half-yokes are assembled of laminated steel 0.5 mm in thickness. The laminations are clamped together by means of steel angles 10 mm thick and end-face steel plates 12 mm thick.

Two copper pipes are intended for liquid nitrogen circulation and cooling the yoke. Two copper plates soldered to the nitrogen pipes are connected to the iron yoke. A high precision of half- yoke assembling is provided by means of 8 pins which are placed on both end-faces of the yoke. The winding is made of a hollow superconducting cable.

66 Fig. 4.3.2.1 Cross-section of the dipole magnet. 1 – iron yoke, 2 – SC bus, 3 – bandage of the winding, 4 – winding, 5 – beam pipe, 6,7 – helium headers, 8 – liquid nitrogen tube, 9 – thermal insulating spacer.

The cable (see Fig. 4.3.2.2) is a 5 mm diameter copper-nickel tube wrapped with 27 superconducting strands. The strands are decoupled into 9 banks with 3 strands in each by means of 9 fishing-lines 0.45 mm in diameter. The cross- section of the strand is shown in Fig. 4.3.2.3. The twist length of the strands is 55 mm. Each strand contains 8910 NbTi filaments 4.5x10-6 m in diameter in the copper matrix. The twist pitch of the filaments is approximately 3 mm. A 0.2 mm diameter synthetic thread is spirally wound with tension around the superconducting strands. The copper-nickel tube with a 4 mm diameter helium cooling channel is wrapped with two layers of 0.04 mm thick Kapton tape. The cable is wrapped with one layer of 0.1 mm thick glassfiber tape impregnated with epoxy compound. The basic characteristics of the superconductor are given in the Table 4.3.2.2.

Fig. 4.3.2.2. Cross-section of the cable. 1 – copper-nickel tube, 2 and 5 – Kapton tape, 3 – SC strand, 4 – insulating fishing-line, 6 – synthetic thread, 7 - glassfiber tape.

67 Fig. 4.3.2.3 Cross-section of the strand.

The saddle-shaped winding has 10 turns of cable or 90 (10 turns x 9 banks) turns of current. All banks of 3 strands in each are connected in series. Three strands of each bank connected in parallel conduct an operation current of 1000 A.

The beam pipe in the dipole magnets is made of stainless steel 0.3 mm in thickness. The needed mechanical rigidity is provided by gluing it to the winding and the bandage. After assembly the cold mass is placed inside the half yokes and pressed by them over the thermal insulating spacers.

Table 4.3.2.2 Basic Characteristic of the Superconductor STRAND superconductor 50% Nb – 50% Ti number of SC filaments 8910 diameter of SC filaments 4.5 m the copper to the SC ratio 1.39/1 twist pitch of filaments 3 mm nominal current at 1.5 T 333 A short sample critical current at 1.8 T 540 A and 4.5 K CABLE cable type hollow composite helium cooling channel diameter 4 mm copper-nickel tube diameter 5 mm insulation Kapton tape thickness 0.04 mm number of banks with strands 9 triplet number of strands 9 x 3 number of insulation fishing-line 9 twist pitch of strands 55 mm banding kapron thread diameter 0.2 mm insulation glassfiber tape thickness 0.1 mm external cable diameter 7.14 mm

68 4.3.2.2. Quadrupole Lens

There are 24 focusing (F) and 24 defocusing (D) quadrupole lenses 400 mm long in the magnetic system of the Booster. The cross-section of the quadrupole lens with hyperbolic poles is presented in Fig. 4.3.2.4. The yoke of the lens consists of four symmetrical parts assembled of laminated steel 0.5 mm in thickness. The production, assembling and cooling of the dipole and quadrupole magnets are similar. The quadrupole and dipole windings, connected in series, are supplied with an equal current of 1000 A.

Fig. 4.3.2.4 Cross-section of the quadrupole magnet in its cryostat.

The superconducting cable of focusing and defocusing lenses comprises only 4 active banks with a triplet of strands. The quadrupole lens winding has only one turn of cable per pole or 4 turns of operation current per pole.

Total electric power required for supply the superconducting magnetic system is less than 1 MW.

4.4. Injection and extraction

The twice repeated single turn injection has duration of 7 µsec per pulse with a betatron stacking in the horizontal plane. The injection scheme includes three bump magnets BM 1  3 and one septum magnet SM (Fig. 4.4.1). The bump magnets form the necessary local distortion of the closed orbit that decreases by two steps during injection time. The time interval between injection pulses is of 0.1 sec.

Fast (single turn) extraction is planned to transfer the beam into the Nuclotron and, when necessary, to the experimental hall for a fixed target experiment performance. It consists of a kicker and a septum magnets (Fig. 4.4.2).

The parameters of the beams at injection and extraction and the magnets are listed in the Tables 4.4.1, 4.4.2.

69 Figure 4.4.1. Injection system layout and beam orbits and envelopes: red – injected beam, violet – ‘bumped” one, blue – circulated beam after first turn injection, green –after accumulation; QD, QF – quadrupole lenses, DIP – dipole magnet, BM 1 3 – magnets for the bump formation, SM – injection septum magnet.

Figure 4.4.2. Fast (one turn) beam extraction from the Booster (green –before acceleration, blue – after acceleration and cooling, red –the extracted beam).

Table 4.4.1. Parameters of the injected and extracted beams. Injected beam Horizonal /vertical emittance of injected beam, π∙mm∙mrad 10/10 Horizontal/vertical emittance of curculating beam, π∙mm∙mrad 100/10 Horizontal/vertical noramlized emittance, π∙mm∙mrad 10/1 Relative momentum spread ±5∙10-4 Extracted beam Horizontal/vertical emittance, π∙mm∙mrad 7.5 Relative momentum spread ±10-4

70 Table 4.4.2. The parameters of the injection and extraction magnets Deflection angle, Magnetic field, T Length, m mrad Injection system ВМ1 6.5 0.0340 0.5 ВМ2 9 0.0340 0.7 ВМ3 6.5 0.0340 0.5 SM 36 0.0940 1 Extraction system Kicker 6 0.125 1.2 SM 10 0.25 1.2

4.5. Collimation

Vacuum conditions in the Booster define significantly ion losses during storage and acceleration. Considering requirements to the vacuum system one has to distinguish among static vacuum (in absence of the ion beam) and dynamic one, when the ion beam circulates in the ring. Ions being lost during injection, storage and acceleration bombard the vacuum chamber walls and knock out atoms (molecules) absorbed by the chamber surface. This process forms the dynamic vacuum condition.

Ion loss occurs due to several reasons: - imperfect beam dynamics in the ring, - ion scattering on residual gas atoms, - ionization or recharge of circulating atoms in collisions with rest gas atoms.

Two last ones depend on vacuum conditions. The ion scattering process plays a minor role in limitations of multicharge ions life time. Main reason of the ion loss is the last process – ionization on the rest gas species. One can estimate the ion life time roughly by the formula

1  rest gas  , (4.5.1) n0 v where and  is the cross-section of the ions ionization in collisions with rest gas atoms of the density n0, v is the ion velocity. The cross-section  depends on the ion velocity (energy) as well – it decreases with the energy growth. For estimates one can accept

-16 2 (Eion) ~ 10 cm at Eion ~ 6 MeV/u. (4.5.2)

5 3 Then at the rest gas pressure 10 pTorr (n0 = 3.53*10 atoms/cm ) the formula (4.5.1) gives

rest gas = 8 s .

This estimate does agree with experimental data for Pb54+ (15 s at P = 5 pTorr).

The U33+ ions appear in the Booster as a result of charge exchange interaction of the circulating U32+ ions with residual gas atoms. One needs to collimate the 33+ ions to keep proper vacuum conditions.

71 A layout of U33+ separation in the horizontal plane and absorption is illustrated in Fig. 4.5.1 in the phase and geometrical spaces. a)

Figure 4.5.1.. Illustration of the ion U33+ collimation in the phase space (a) and the collimator geometry in the horizontal plane (b). 1 – x co-ordinate of collimator entrance, 2 – thickness of the collimator, the line colors in the Fig. b) correspond to color in the Fig. a).

To obtain the 100% absorption of the U33+ ions only on the collimators, it takes at the least eleven collimators per arc. The location of the collimators and distribution of the ion absorption are shown in the Fig. 4.5.2. The lower part of Figure shows the arc lattice, the location of eleven collimators (markings C1,…C11), the horizontal envelope of the beam of ions with Z = 32 (dark color) after injection and horizontal envelope of trajectories of ions with Z = 33 (sky blue color). The figure shows the process of absorption of ions with Z = 33 on the collimators. They are located on the inner part of chamber and ratio of the collimator edge co-ordinate Xcolim to the beam envelope Xenv at the collimator azimuth is 1.2. The following markings are adopted in the Figure. Focusing and defocusing quadrupoles are marked QF and QD, the number after this marking shows period number in the arc. The label Dip is adopted for the dipoles.

Figure 4.5.2. Ion absorption distribution for eleven collimators (the 100% collimation efficiency). Percentage shown with upper and bottom lines indicates losses on the lattice magnets and collimators.

72 This figure indicates as well, that the each of the collimators C5, C7, C9 and C11 absorbs a small quantity of the U33+ ions (about 3% each). If these collimators are removed, the collimation efficiency is equal 98.6%. The additional removal of the collimator C1, which catch 6.3% of the U33+ ions, reduces the collimation efficiency to 94.9%. The further decreasing the number of collimators reduces the collimation efficiency strongly. The variant with 6 collimators per arc and the collimation efficiency of 94.9% is shown in the Fig. 4.5.3.

Figure 4.5.3. Ion absorption distribution for six collimators and the 94.9% collimation efficiency.

On this figure the deal of ions with Z=33 is absorbed by lattice elements QF1, QF2, QF4, QF5 and QF6. The total part of these ions is 5.1% (losses=5.1%)

4.6. Beam acceleration. RF system

The Booster RF cycle is composed of four parts: - the adiabatic trapping at fixed frequency (flat bottom), - the beam acceleration at the forth harmonics of the revolution frequency up to 100 MeV/u and debunching, - the beam bunching at the first harmonics of the revolution frequency together with the electron cooling, - the beam acceleration at the first harmonics of the revolution frequency up to 400 MeV/u.

4.6.1. Adiabatic trapping

The unbunched beam from linac (Δφ = 3600) is trapped with the use of the adiabatic trapping process [4.6.1]. The process is called adiabatic when its duration is long compare to the synchrotron period Ts. At the beginning of the process the small RF voltage Vi is established. Vi is small enough for the correspondent bucket area Ai to be (much) smaller then the initial beam emittance. The special coefficient for the trapping process c is defined as:

dA dt = ac . (4.6.1) A Ts

73 This coefficient should be much smaller than 1 for the adiabaticity condition to be approached.

When the RF voltage is raised from Vi to its final value Vf keeping αc constant (so called isoadiabatic law) the voltage variation is given by:

V V( t ) = f 2 . (4.6.2) 轾 V f - a t 臌犏 Vi T s

The parameters for the trapping process are chosen to satisfy the following criteria: the capture efficiency has to be near to 100%. The longitudinal emittance increase (the beam dilution) has to be minimum. The duration of the trapping process should have reasonable limits.

The following parameters of trapping were chosen: α = 0.38 , Vi = 50 V, Vf = 2000 V. The simulation results obtained with ESME program [4.6.2] under conditions listed in the Table 4.6.1 show a theoretical 100% efficiency (see Fig. 4.6.1, 4.6.2).

74 Figure 4.6.1. Distribution of particles in phase space during adiabatic trapping at the start and at the end of the process.

Figure 4.6.2. rms bunch length during adiabatic trapping.

Table 4.6.1. Adiabatic trapping, main parameters Number of injected particles 4·109 Injection energy (MeV/u) 6 Revolution frequency (MHz) 0.160 Revolution period (μs) 6.96 Bunch rms emittance(eVs) 1×4 Harmonic number 4 Stable phase 0

Vi/Vf (kV) 0.05/2 dp/p at injection ±0.0005 dp/p after capture ±0.0013 Trapping time (ms) 25

Synchrotron period Ts at end (ms) 0.5 Adiabaticity coefficient α 0.38

4.6.2. First stage of acceleration

The first stage of acceleration begins just after adiabatic trapping and finishes at the energy suitable for the electron cooling (100 MeV/u). The variation of the magnetic field is chosen to be composed of lineal ramp of 1 T/s and two parabolic parts 40 ms each – transitions from the flat bottom and to the flat top for debunching and electron cooling. The starting value for the voltage variation during transition from the flat bottom to the lineal magnetic field ramp is defined by the previous trapping process. The final value is suitable to choose so that the stable synchronous phase is near 300 (sinus wave) i.e. approximately 7 kV. Computer simulations show good results even for the lineal voltage variation from 2 kV to 7 kV. Similarly deceleration is accompanied by lineal voltage decrease from 7 kV to 1 kV just before the debunching. During the first stage of acceleration the RF frequency is varied from 640 kHz at the injection up to

75 about 2.4 MHz. Main parameters of the ion beam and the Booster RF system are summarized in the Table 4.6.2.

Table 4.6.2. Characteristic parameters for the fist stage of acceleration in the Booster Number of particles 6·109 Energy (MeV/u) 6/100 Momentum (MeV/s) 105/440 Magnetic rigidity (Tm) 2.85/11.7

RF frequency fRF (MHz) 0.640/2.400 Bunch rms emittance (eVs) 1×4 Harmonic number 4 Stable phase (lineal ramp) 27.5 Vmax/Vmin (kV) 7/1 Freq. swing 4

Bdot max (T/s) 1 Acceleration duration (s) 0.64

4.6.3. Beam bunching at 1st harmonics and electron cooling

The process of the electron cooling is discussed in details in the chapter 4.9.

4.6.4. Second stage of acceleration

In the collider the longitudinal rms emittance must not exceed 3 eVs so after the electron cooling it has to be no more than 2 eVs to make allowance of the inevitable emittance growth (factor 1.5) on the stripping foil, during beam matching in the Nuclotron and collider and due to the various other reasons. The RF frequency varies from 600 kHz up to 1 MHz. The magnetic field variation has two parts: 40 ms parabolic part and the lineal ramp at 1 T/s. The RF voltage is assumed to vary lineally from 1 kV to 7 kV during the parabolic variation of the magnetic field and to be the constant 7 kV (maybe less) during the lineal magnetic field ramp (Table 4.6.3).

Table 4.6.3. Characteristic parameters for the second stage of acceleration in the Booster Number of particles 6·109 Energy (MeV/u) 100/400 Momentum (MeV/s) 440/950 Magnetic rigidity (Tm) 11.7/25.2

RF frequency fRF (MHz) 0.600/1.00 Bunch rms emittance(eVs) 2 Harmonic number 1 Stable phase (lineal ramp) 27.5 Vmax/Vmin (kV) 7/1 Freq. swing 1.66

Bdot max (T/s) 1 76 acceleration time (s) 0.92

4.6.5. Acceleration system

Nearest prototype of the Booster acceleration system is that one for SIS-100 designed by GSI in collaboration with BINP (Novosibirsk). Due to cost and reliability consideration the optimum is to use a ferrite loaded cavity for the acceleration. The cavity consists of two coaxial quarter- wave resonators, working in push-pull mode onto a common accelerating gap (Fig. 4.6.3). The resonant frequency of the cavity is controlled by DC biasing of the air cooled ferrite stack. In the frequency range from 0.6 to 2.4 MHz the accelerating voltage of 7 kV is necessary due to beam dynamic requirements. The parameters of the cavity based on ferrite rings produced by Russian industry are listed in the Table 4.6.4.

Fig. 4.6.3. Schematics of the cavity and RF generator. 1 – phase discriminator, 2 – biasing amplifier.

Table 4.6.4. Parameters of the Booster acceleration RF system. Harmonics number 4/1 Frequency range, MHz 0.6 – 2.4 Maximum voltage, kV 7 Number of cavities 1 Length of the cavity, m 3.9 Ferrite ring parameters: Inner diameter, mm 153 Outer diameter, mm 202 Width, mm 25 Permeability 10 Initial permittivity 200 77 Equivalent quality factor 8 Power consumption, kW 1.15 Cooling of ring core Air, direct

The RF power supply can be designed on the basis of GU92-A electronic tube. Due to relatively small heating power in the ferrite the air cooling can be applied. The inner cylinder of the cavity can be designed as a double wall pipe (Fig. 4.6.4). The air flux moving through the halls in the outer wall cools the inner and side surfaces of the ferrite rings.

Figure 4.6.4. Air cooling of the ferrite stack. 1 – air flux, 2 – ferrite rings.

4.7. Tune shift at injection and at extraction

The incoherent space charge tune shift can be estimated by well-known formula

2 Z rp N Q   2 Fsc Fb , (4.7.1) A 4  n

where Z and A are the ion charge and mass numbers correspondingly, rp is the proton classic radius, N is the total number of the ions in the ring, n is the normalized rms beam emittance, Fsc – image force correction factor, Fb - the bunching factor that is equal to the ratio of peak bunch current to the mean one:

CRing / h Fb  , (4.7.2) 2 s

CRing is the Booster ring circumference, h is harmonics number, s is the rms bunch length. Assuming Fsc ~ 1 one can estimate acceptable normalized beam emmitance at the injection into the Booster:

2 Z rp N  Fb  n  2 . (4.7.3) A 4 Qmax

78 We need to store in the booster up to 4109 of U32+ ions at the energy of about 6 MeV/u. At Qmax ≤ 0.05 and Fb = 2 one has to provide the normalized beam emittance n  0.74 mmmrad. This value is slightly larger than that one expected at the exit of the linear injector and corresponds to the unnormalized 95% (6-sigma) emittance   39 mmmrad. That is a few times smaller than the Booster acceptance (Table 4.2.1).

The reserve option of the injection chain operation presumes storage in the Booster of 2109 U64+ ions. In this case the tune shift of 0.05 corresponds to the emittance value of n = 1.5 mmmrad, or 95% unnormalized emittance of about 78 mmmrad. This value is comparable with the vertical booster acceptance and corresponds to the limit value if a larger tune shift value can not be reached due to the beam instability. One should note that in this case the electron cooling time will be shorter because of its Z2 dependence.

At the energy of the electron cooling application (about 100 MeV/u) the emittance of the U32+ can be decreased to the value of about n  0.16 mmmrad limited by the tune shift at this energy. So small emittance is not acceptable for the experiment because of very high bunching factor in the collider: minimum unnormalized emittance value required at 3.5 GeV/u of the experiment energy is equal to about 1.3 mmmrad. Therefore one needs to take a care about stabilization of the emittance during the cooling. It can be done, for instance, by the cooling with misaligned electron beam (see chapter 4.9).

To avoid a sufficient increase of the bunch longitudinal emittance at crossing the stripping foil the bunch length after acceleration to the maximum Booster energy has to be as small as possible. The bunch intensity at the injection into the Nuclotron decreases due to partial ion loss in the stripping foil and will be slightly larger than 109. For the fully stripped uranium ions at the rms normalized emittance of 1.3 mmmrad the rms bunch length has to be larger than about 6 m to keep the tune shift in the Nuclotron below 0.05.

4.8. Emittance growth after crossing the stripping foil

As a prototype of the stripping target design the RHIC stripping foil was chosen. At the RHIC two types of the foil were tested for the gold ion stripping at 70 MeV/u [4.8.1]. In routine operation the carbon foil of the thickness of 120 m is used. The foil thickness is larger than the optimum one: such a value was chosen to provide a long life-time of the foil.

The ion interaction with the target leads to an increase of both - transverse and longitudinal beam emittances. The first one increases due to ion multiple scattering on the target atoms. The second one grows up due to two effects: the fluctuations of the ionization energy loss (“the energy straggling”) and non-uniformity of the foil thickness provoking variation of the ionization loss with the ion position at the target. The rms non-uniformity of the carbon foil is about 5% and the growth of the longitudinal emittance due to this effect is about three times larger than due to the energy straggling. The situation can be sufficiently improved by using of silica foil of precise thickness (of the non-uniformity below 0.5%). The experimental investigations done at BNL [4.8.1] show that the longitudinal emittance of the gold beam after crossing the silica foil of the thickness of 100 m is about three times less than after crossing the carbon foil.

Here we analyze the transverse and longitudinal emittance growth of the uranium beam at 400 MeV/u after crossing of both types of the foils: carbon foil of the thickness of 125 m and silica foil of 100 m. The ion charge state changes inside the foil and for an accurate calculation

79 of the emittance growth one needs to integrate the ionization loss and multi-scattering cross- section over the ion trajectory in the target. However one can calculate the upper estimate for the maximum charge state only. Therefore we present here the results for the emittance growth of the U92+ ions that slightly overestimate real situation. The rms parameters of the scattering process were calculated in accordance with [4.8.2]. The expected longitudinal and transverse emittance growth after crossing the foils of two kinds is presented in the Table 4.8.1.

Table 4.8.1. Change of the U92+ beam emittance after crossing the stripping target carbon silica Thickness, m 125 100

Foil Rms non-uniformity t , % 5 0.5

Ionization energy loss EBB, MeV 320 397

tEBB, MeV 16 1.99

Rms ion energy straggling Estr, MeV 3.76 4.38 E, MeV 16.4 4.81 Rms ion multiscattering angle 1.2210-4 2.0210-4

Longitudinal emittance growth at s = 7 m, eVs 1.69 0.493 -3 -2 Normalized transverse emittance growth at t = 1 m, mmmrad 7.7610 2.1310

As shown above the minimum normalized transverse emittance required at the experiment is about 1.3 mmmrad and the emittance growth after the foil crossing is negligible at the beta function at the foil position of a few meters.

The longitudinal emittance required for a successful bunch compression in the Nuclotron is about 3 eVs. At the large foil non-uniformity the increase of the longitudinal emittance after crossing the target has to be taken into account. The required longitudinal emittance value after the electron cooling can be estimated using the following expression for the final emittance ||,f :

2 2  ||, f   ||,0   || ,

where ||,0  2.5 eVs.

4.9. Electron cooling system

The main goal of the Booster electron cooler is the decreasing of the longitudinal emittance from the injection value of about 7.5 eVs to the necessary value of 2.5 eVs. Cooling time is limited by the operation cycle of the Booster and can not exceed the value of 1 sec. For the transverse plane the cooling system has to keep the value of the normalized transverse emittances at the level of 1 mmmrad (rms). For the stabilization of the transverse emittance the misalignment of electron and ion beam axes is proposed on the level of about 1 mrad in both transverse planes.

4.9.1. Ion energy choice for electron cooling application

80 Ion energy in the Booster ranges from 6 MeV/u to 400 MeV/u that corresponds to the electron energy range 3.27  217.86 keV. Choosing an optimal energy value for electron cooling one has to account the following effects: 1) beam lifetime limitation due to interaction with the rest gas ; 2) beam lifetime limitation due to recombination on the cooling electrons; 3) space charge effects appearing due to ion beam shrinking at cooling; 4) sufficiently short cooling time (≤1 sec); 5) space charge effect of electron beam on ion cooling; 6) an optimal use of the RF station (see this section, below) ; 7) cost of the electron cooler.

In the range of so called large ion velocity the electron cooling time increases with the ion (electron) energy as following [4.9.1]:

2 3 / 2   i  ecool  C  , (4.9.1) Je where C is the constant depending of the cooler design (electron beam and magnetic field quality, etc.),  and  are the Lorentz factors, i is the normalized ion beam emittance, Je is the electron current density. “Theoretically” reasoning the last one can be increased with energy as energy in power 3/2 (the Child-Langmuir law). However, as practice of electron coolers shows, in the electron energy range quoted above one can have an effective cooling with Je ~ 10 2 2 mA/cm at 2.5 keV (LEAR electron cooler) and with Je ~ 100 mA/cm at 70 keV (COSY 0.7 1/3 electron cooler). That scales with energy much slower - as (Ee) , or  . Thus, one can believe the cooling time dependence on ion energy is given (in the quoted energy range) by the following formula:

2/3 1/3 ecool    (Eion) . (4.9.2)

Now we can begin the choice of the electron cooler energy based on the effects mentioned above.

1) Ion lifetime is sufficiently long even at injection energy (paragraph 4.5). Therefore thr limitation by interaction with the rest gas does not play a significant role in the choice of electron cooler energy.

2) Ion recombination on the cooling electrons is almost independent of the energy (when neglecting with Lorentz transformation for time: 1 < γ < 1.4 in the ion energy range for the Booster). Therefore, this effect does not define a choice of the cooler energy (nevertheless, it is critical for the ion life time – see section 4.9.2).

3) Space charge tune shift grows up when the ion beam emittance decreases at cooling (see Formula 4.7.1). Due to this reason we can not use the electron cooling at injection energy when the ion beam intensity is near the limit by tune shift. However, we need to cool the beam later to obtain a sufficiently small ion momentum spread for formation of short bunches after acceleration in the Nuclotron (section 5.3.2). Therefore, one has to cool the ion beam at certain acceleration when the factor 2 decreased tune shift by two times at least. It gives us

cool > 2injection, or Ecool > 4Einjection = 24 MeV/u . (4.9.3)

81 4) Provision of a sufficiently short cooling time (≤1 sec) can be done in all the energy range because of rather slow dependence of cooling time on energy (4.9.2).

5) The space charge effect of the electron beam plays an important role when its space charge parabola produces electron energy shift across the beam larger than the energy spread of the ion beam. Such an energy shift (difference of electron energy on the beam axis and its border) is given by the formula

30  Ie [ A] E   . (4.9.4) e [ eV ] 

So, for the electron energy of 54 keV ( = 0.427) and electron beam current of about 1 A it gives E  70 eV (E/E  1.3×10-3) that may have an essential impact on the cooling process.

6) Ion acceleration in the Booster is proposed to be performed in two steps (Paragraph 4.6): on 4th harmonics of the revolution frequency up to the cooler energy and on the 1st one after the cooling. It would be convenient to use the same RF system on both steps of the acceleration. That would be possible if the cooler energy (Eion)cool is sufficiently high. At the Booster parameters such an opportunity appears if (Eion)cool 100 MeV/u.

7) The cost of the electron cooling system has rather smooth dependence on the electron energy for the standard scheme of the cooler. The price of the Booster cooler can be estimated on the level 1÷1.2 M$.

A cooler of electron energy of 50 keV planned for the Booster can be constructed by a conventional (“standard”) scheme. As a prototype one can consider the cooler (Fig. 9.4.1) designed and constructed at Budker Institute of Nuclear Physics (Novosibirsk) for Institute of Modern Physics (Lanzhou, China) [4.9.2].

Fig.4.9.1. Electron cooler EC-35 (BINP, Novosibirsk) 1 – electron gun, 2 – electrostatic plates for compensation of centrifugal drift, 3- toroidal solenoid, 4 – straight solenoids, 5 – magnetic shield, 6 – collector, 7 – ion beam orbit magnetic correctors, 8 – ion beam channel.

82 4.9.2. Recombination in the cooler section

At the electron cooling of heavy ions the recombination - i.e. capture of cooling electrons by ions - results in loss of the ions due to change of their charge and deformation of the ion closed orbit. The theory of the electron-ion recombination is well elaborated for fully stripped ions [4.9.3]. In the case of partially charged ions the recombination rate can be interpolated from the experimental data.

Measurements of electron recombination rates for Pb52+, Pb53+ and Pb54+ ions were done at LEAR (Fig.4.9.2 [4.9.4]). The ion energy in these experiments was of 4.2 MeV/u, the ring circumference of 78.54 m, the vacuum pressure of 2×10-11 Torr.

Fig.4.9.2. The dependence of the recombination rates on the electron beam current for different charge states of lead ions.

For the charge state Pb54+ the number of electrons on electron shells is 28 and the electron structure is 1s2 2s22p6 3s23p63d10, which corresponds to three closed electron shells. For the charge state Pb53+ one electron stays on the forth shell that decreases the recombination time very significantly. The lifetime for the charge state Pb52+ (two electrons on the fourth shell) is 54+ comparable with the charge state Pb (Fig.4.9.2). The recombination coefficient rec is defined usually by the formula

dn rec    n  n . (4.9.5) dt rec ion e

Then the recombination time is equal to

1 dnrec  rec    rec  ne (4.9.6) nion dt

83 Here nrec is density of recombined ions, nion , ne are the densities of recombining ions and electrons. Table 4.9.1 gives experimental values of rec [4.9.4] and theoretically estimated ones with Bell's formula [4.9.3]. One can see a great discrepancy of experiment and theory that demonstrates a complexity of the problem.

Table 4.9.1. Experimental and theoretical recombination coefficient values, ion energy 4.2 MeV/u, transverse electron temperature 0.2 eV. Ions kind Experiment Bell's formula 10-8 cm3s-1 10-8 cm3s-1 Pb52+ 11 2.25 Pb53+ 60 2.29 Pb54+ 9 2.32 U28+ 10 1.8 Au25+ 10 1.3

The U32+ ions assumed to be cooled in the Booster have the electron shell structure 4s24p64d104f14. That corresponds to 4 closed electron shells. According to LEAR experimental results (Table 4.9.1) one can expect the recombination coefficient

-8 3 rec  1010 cm /s .

An electron beam of 1 cm radius, of 1 A current and electron energy of 54 keV has the electron 8 -3 density ne  1.510 cm . This gives us according (4.9.6)

rec = 15 s .

That is sufficient for our goal.

4.9.3. Design of the Booster electron cooler

Parameters of the proposed electron cooling system are very close to those ones of the existing cooling system EC-35 presented above (Fig. 4.9.1 and Table 4.9.2). It consists of the following main subsystems: electron beam formation system including the electron gun (pos.1); electron collector (pos.6); magnetic system containing straight solenoid (pos.4), toroidal solenoids (pos.3), bending field coils and electrostatic plates for drift compensation in bending toroids (pos.2), coils for the electron beam position correction; vacuum system, which consists of vacuum chambers and vacuum pumps, as well as of tools for vacuum chamber heating and for pressure measurement; diagnostics system including two pairs of pickup stations at the entrance and the exit of the cooling section; water cooling system providing cooling of the solenoids, the collector, the electron gun anode and the radiators of air cooling and distillate water cleaning system; high voltage power supplies; mechanical supports. Two pairs of dipole magnets will be installed in the cooler section of the Booster to correct the ion beam trajectory displacement produced by vertical components of the cooler toroid field (pos.7).

84 For simulation of the optics of the electron guns and electron collectors both BINP and JINR electron cooling groups use mostly the special code SAM [4.9.5]. The code allows to simulate the electron trajectories taking into account the geometry of electrodes, the longitudinal magnetic field and the field of the electron beam space charge. As result of a simulation one can obtain distribution of the electron beam density and variation of the electron transverse velocity across and along the beam. Two examples of such simulations are presented in the Fig.4.9.3.

Table 4.9.2. Main parameters of electron cooler. Maximum electron energy, keV 60.0 Beam current, A 0  1.0 Power consumption, kW 100 Beta functions in cooling section, m 8 / 8 Dispersion function in cooling section, m 0 Cooler overall length, m 4.0 Effective length of the cooling section, m 2.5 Magnetic field in the cooling section, kG 1.5 Magnetic field non-homogeneity in the cooling section 110-4 Electron beam radius in the cooling section, cm 1.0 Transverse electron temperature, meV 200 Longitudinal electron temperature, meV 0.5

Fig.4.9.3. Simulation of electron trajectories in the gun and collector for EC-35 performed with the SAM program [4.9.6]. Red – electrodes and electric field equipotential lines, blue – electron trajectories, green – magnetic shield and magnetic field distribution along the collector axis.

4.9.4. Stabilization of the ion beam emittance with electron cooling

Electron cooling applied to the ion beam in the Booster has a specific feature. As said above, it has to decrease ion momentum spread and to keep (almost) constant the ion beam emittance to

85 avoid increase of the space charge tune shift (Paragraph 4.7). A few different methods are known for stabilization of the emittance at required value when the electron cooling is applied: - use of a “hollow” electron beam with a special electron density distribution across the beam: it is very low near the beam axis and grows up in the outer part, - application of white noise in transverse degree of freedom in order to shift equilibrium between cooling and heating into the region of larger emittance value, - misalignment of the electron beam (introduction of some angle between electron and proton beam axes in the cooling section).

The “hollow” beam application [4.9.7] is supposed to be very efficient for ion beam storage using cooling-stacking procedure. In this case low electron density in the stack region (near the electron beam axis) permits to avoid “overcooling” the stack and decreases (for heavy ions) recombination rate in the cooling section. However, main restriction on the “hollow” beam application is related to the fact that significant part of the ions are crossing the cooling section in the region of non-linear electric field of the electron beam outer part. That can provoke additional ion loss due to “electron heating” effect.

The heating of the transverse degree of freedom by additional noise were used at a few rings to suppress a coherent instability of the cooled ion beam. However it was shown that the transverse heating decreases the beam life-time as well and leads usually not only to increase of the emittance, but the momentum spread also.

As it is shown in many experiments the electron beam misalignment is a powerful tool to control emittance of the ion beam [4.9.8]. However, at small angles the misalignment leads to decrease of the cooling efficiency only, but the beam emittance is determined by an equilibrium between cooling and heating due to intrabeam scattering. When the misalignment reaches a certain threshold value a qualitatively different situation takes place: the amplitude of the ion betatron oscillations grow up to certain value that depends on the misalignment angle. Therewith, the beam emittance value (independently of an additional heating presence) corresponds to the oscillation amplitude. In absence of another “heating” effects the beam profile has specific double-peak structure. The sudden appearance of this structure at increase of the misalignment angle was called “monochromatic instability” observed in first experiments at NAP-M [see, for instance, 4.9.1]. Simulations with the BETACOOL program demonstrate also development of the monochromatic instability (see section 4.9.4 below). However, as the experiments at S-LSR cooler ring (Kyoto University) have shown, the measured beam profiles have practically Gaussian shape up to very large misalignment angle (Fig. 4.9.4) [4.9.8]. It can be explained by peculiarities of the intrabeam scattering process, which leads to very fast relaxation of the distribution function to the equilibrium Gaussian shape.

86 Fig. 4.9.4. Transverse beam profiles measured by the ionization monitors on S-LSR storage ring, proton energy is of 7 MeV, the electron current is of 25.5 mA, horizontal misalignment angles [mrad] are : -1 (red), -0.5 (blue), 0 (green), 0.5 (cyan), 1 (pink), 1.5 (violet), 2 (yellow), dash curve is the Gaussian extrapolation.

4.9.5. Simulation of cooling process with BETACOOL

BETACOOL software [4.9.9] was developed for simulation of ion beam parameters in a storage ring taking into account peculiarities of electron, stochastic and laser cooling, intrabeam scattering (IBS), ion beam interaction with residual gas, internal target and colliding beam (in a collider mode of the ring operation). General goal of the BETACOOL program is the simulation of long (comparatively to the ion revolution period) processes, which lead to variation of the ion distribution function in 6-dimensional phase space. The ion beam motion inside a storage ring is supposed to be stable and it is treated in linear approximation.

BETACOOL code is being developed by JINR Electron Cooling group since 1995 in the frame of collaborations with different scientific centers: BINP (Novosibirsk, Russia), ITEP (Moscow, Russia), CERN, RIKEN (Japan), FZJ (Germany), NIRS (Japan), Kyoto Univ. (Japan), BNL (USA), Fermilab (Batavia, USA), GSI (Darmstadt, Germany), Erlangen Univ. (Germany), Uppsala Univ. (Sweden). The program was and is being used for optimization of the cooling process of the existing cooling devices and design of the new electron coolers [4.9.10].

The simulation of the electron cooling of 238U32+ ions in the Booster at the parameters listed in Table 4.9.3 does demonstrate the effect of misalignment of the electron beam (Fig. 4.9.5-4.9.6).

Table 4.9.3. Main parameters of simulation of the electron cooling process in the Booster Ion energy, MeV 100 Ion kind 238U32+ Particle number 2×109 Initial transverse emittance,  mm mrad 1.5 Initial momentum spread 5×10-4 RF voltage, kV 10 Initial bunch length, m 14

87 Electron beam current, A 1.0 Electron beam temperature long/trans, meV 200 / 0.5 Misalignment of ion and electron beams axes 5×10-4

One can see that after 1 sec of cooling the transverse emittance (Fig.4.9.5a) and momentum spread (Fig.4.9.5b) reach the equilibrium between the cooling and IBS heating. The necessary longitudinal emittance of about 2.5 eVs can be reached in less than 1 sec of the cooling process (Fig.4.9.5c). a) b) c)

Fig. 4.9.5. Evolution of the bunched ion beam parameters during the cooling process with misalignment angle of 5×10-4. a) horizontal (red) and vertical (blue) emittances, b) ion momentum spread, c) longitudinal emittance. The beam profile at cooling with misaligned electron beam has a well pronounced double peak structure and most of the particles oscillate with equal amplitudes in the horizontal plane. (Fig.4.9.6a). Due to misalignment the transverse cross-section of the cooled ion beam has a rectangular form (Fig. 4.9.6b), but their transverse phase space looks as elliptical one (Fig. 4.9.6c).

a) b) c) Fig.4.9.6. Ion beam density distribution after 2 seconds of the cooling: a- horizontal (red) and vertical (blue) profiles, b -transverse plane and c – horizontal transverse phase space of the cooled ion beam

The optimum regime can be found from the dependence of the cooling time on misalignment angle when the longitudinal emittance decreases from 7.5 eVs to necessary value of 2.5 eVs (Fig. 4.9.7). The cooling time has to be less than 1 sec and the transverse emittance has to be about 1  mm mrad. For the misalignment angle 0.5 mrad the cooling time does not decrease too much and the transverse emittance is sufficiently large to avoid a tune shift resonance.

1.8 1.8

cooling time

1.6 1.6

d emittance

c 1.4 1.4 e m

1.2 1.2 , m e m

m 1 1 i i t p

, g 0.8 0.8 e n i c l n

o 0.6 0.6 a t o t c 0.4 0.4 i m 0.2 0.2 e 0 0 0.E+00 2.E-04 4.E-04 6.E-04 8.E-04 1.E-03 misaligment, rad

Fig.4.9.7. The dependence of the cooling time and transverse emittance after the cooling process on the misalignment angle between electron and ion beams axes; “the cooling time” is defined as a time interval when the longitudinal emittance decreases from 7.5 eVs to 2.5 eVs (see Fig.4.9.5).

Summary

The electron cooling can not be applied at the ion injection energy of 6 MeV/u due to large tune shift that appears under an action of the cooling. The proposed cooling energy of 100 MeV/u allows to avoid this problem and provides the cooling time of about 1 sec. For the electron cooler of the electron energy of 54 keV the standard design can be used.

4.10. Schedule of the works. Estimated cost

The Booster Technical Design Report preparation is scheduled for 2008 -2009. Due to the application of the magnet design developed for IHEP and ITEP boosters the TDR does not require a long R&D stage.

The disassembling of the Sinchrophasatron coils will be performed during the same period.

Manufacturing of the Booster magnetic, vacuum and RF systems will be provided during 2009- 2010.

The assembly and commissioning are scheduled for 2011 – 2013.

The cost of the Booster magnetic system fabrication in the JINR machinery workshop is estimated preliminary as 2.6 – 3.6 $M. Other more expensive subsystems are the vacuum, RF and extraction ones. Their cost will be estimated accurately at the technical design stage.

The nearest prototypes of the Booster electron cooling system are the EC-35 cooler constructed by BINP and ITEP cooler designed by the JINR electron cooling group. The cost of the first one was slightly below 1 M€, estimated cost of the second one was about 0.85 $M

The estimated cost of the Booster construction including the electron cooling system is about 8 $M.

89 4.11. References

4.3.1. A.M.Baldin et. al., Heavy ion accelerator complex, JINR preprint 9-11796, Dubna 1978. 4.3.2. N.N. Agapov, A.M. Baldin, H.G. Khodzhibagiyan, A.D. Kovalenko, V.N. Kuzichev, V.A. Mikhailov, and A.A. Smirnov, «Low field cold iron SC-magnet technology: New aspects of application,»IEEE Trans. Appl. Supercond..vol. 10, N 1, pp.280-283, 2000. 4.3.3. A.D. Kovalenko, «The concept of an intermediate temperature iron SC-magnets,» VLHC Magnet Workshop, Batavia, USA, May 2000, submitted for publication.

4.6.1. 1. A.V.Eliseev, I.B.Issinsky, A.D.Kovalenko, V.I.Volkov. Investigations of possibilities of Nuclotron’s beam intensity Increase by optimization of capturing into acceleration. Proc. of the 7-th International Workshop. Stara Lesna, Slovak Rep., “Relativistic Nuclear Physics from Hundreds of MeV to TeV”, 2003. pp. 91-96. 4.6.2. http://www-ap.fnal.gov/ESME/

4.8.1. C. Montag, L. Ahrens, P. Thieberger, Tomographic measurement of longitudinal emittance growth due to stripping foils, Proceedings of 2005 Particle Accelerator Conference, Knoxville, Tennessee. 4.8.2. F. Hinterberger, D.Prasuhn, Analysis of internal target effects in light ion storage ring, NIM A 279(1989), 413-422.

4.9.1. K. Kilian and D. MShl, Lecture Notes in Physics 178 (1983) 163. 4.9.2. X.D.Yang, V.V.Parkhomchuk, et al., Commissioning of Electron Cooling in CSRm. Proc. of COOL'07 (2007). http://www.cool07.gsi.de 4.9.3. S. Baird, J. Bosser, C. Carli, I. Meshkov I, D. Möhl, et al. Measurement of the lifetime of Pb52+, Pb53+ and Pb54+ beams at 4.2 MeV per nucleon subject to electron cooling. Physics Letters B 361 (1995) 184-186. 4.9.4. X.D.Yang, V.V.Parkhomchuk, et al. Commissioning of Electron Cooling in CSRm. Proc. of COOL'07 (2007). http://www.cool07.gsi.de 4.9.5. B.Fomel, M.Tiunov, V.Yakovlev. SAM – an interactive code for evaluation of electron guns. Preprint BINP 96-11, Novosibirsk (1996) 4.9.6. A.Ivanov. PhD Thesis. BINP, Novosibirsk (2007). 4.9.7. A.Bubley, V.Parkhomchuk, V.Reva. Advantages of electron cooling with radially varying electron beam density. Nucl. Instr. and Meth. A532 (2004) 303-306. 4.9.8. A.Smirnov, I.Meshkov, A.Sidorin, A.Noda, et.al. Investigation of ordered proton beams at S-LSR. Preprint NIRS, HIMAC-126 (2007). 4.9.9. I.Meshkov, I.Seleznev, A.Sidorin, A.Smirnov, E.Syresin, G.Trubnikov. BETACOOL program for simulation of beam dynamics in storage rings. Nucl. Instr. and Meth. A 558 (2006) 325-328. 4.9.10. A. Sidorin: Cooling Simulations with the BETACOOL Code. Proc. of COOL'07 (2007). http://www.cool07.gsi.de