Institute for Nuclear Research and Nuclear Energy,
72 Tzarigradsko Shaussee Blvd., Sofia – 1784, Bulgaria
E – mail: firstname.lastname@example.org
ПРОЦЕССЫ ПРИ УСКОРЕНИИ ТЯЖЕЛЫХ ИОНОВ ДО ВЫСОКИХ ЭНЕРГИЙ Д. Динев
Болгарская академия наук,
Институт ядерных исследований и ядерной энергетики,
Цариградское шоссе 72, София – 1784, Болгария
E – mail: email@example.com
A review of processes that occur in high energy heavy ion acceleration by synchrotrons and colliders and that are essential for the accelerator performance is presented. Interactions of ions with the residual gas molecules/atoms and with stripping foils that deliberately intercept the ion trajectories are described in details. These interactions limit both the beam intensity and the beam quality. The processes of electron loss and capture lie at the root of heavy ion charge exchange injection. The review pays special attention to the ion induced vacuum pressure instability which is one of the main factors limiting the beam intensity. The intrabeam scattering phenomena which restricts the average luminosity of ion colliders is discussed. Some processes in nuclear interactions of ultra-relativistic heavy ions that could be dangerous for the performance of ion colliders are represented in the last chapter.
Представлен обзор процессов, которые имеют место при ускорении тяжелых ионов до высоких энергий синхротронами и коллайдерами и которые в значительной мере определяют параметры ускорителя. Большое внимание уделено процессам взаимодействия ионов с молекулами и атомами остаточного газа и с перезарядными мишенями. Эти взаимодействия ограничивают как интенсивность так и качество пучков. Процессы потери и/или захвата электронов лежат в основе метода перезарядной инжекции тяжелых ионов. Обсуждается вызванная ионами нестабильность давления остаточного газа. Эта нестабильность давления является одным из основных факторов ограничивающих интенсивность пучков. Рассматривается внутрипучковое рассеяние ионов. Это явление ограничивает средную светимость ионных коллайдеров. В последнем разделе обсуждаются некоторые процессы при ядерных взаимодействиях ультрарелятивистких пучков тяжелых ионов, которые могут ограничивать достижимые параметры ионных коллайдеров.
1. Introduction Historically the investigations with accelerated beams of heavy ions began with nuclear structure studies and with synthesis of new transuranium elements. For these experiments one needs ion energies, which lie slightly above the Coulomb barrier. Tandems, linear ion accelerators and cyclotrons were used at the early times of research with heavy ion beams. Very soon the scientific interest broadened toward more deep and sophisticated experimental studies in the fields of atomic and nuclear physics and applications in cancer therapy.
When the available ion energy surpassed the 1 GeV/u threshold studies of the nuclear equation of states and search for very hot and dense nuclear matter and for phase transitions began.
In this review we will restrict ourselves to the problems of acceleration of heavy ions to relativistic energies, i.e. to more than 1 GeV/u. This is done by synchrotrons.
For energies above about 10 GeV/u the fixed target mode becomes inefficient and colliding of heavy ion beams must be used.
The first synchrotrons accelerating ions, Synchrophasotron in JINR, Bevatron in LBNL and Saturn – II in Saclay, were proton machines converted to ion synchrotrons. The first two machines were weak focusing accelerators. The upgrade included improvement of the vacuum and building of new injectors but in spite of these measures only bare nuclei could be accelerated due to the poor vacuum conditions. The maximum energies were: 1.15 GeV/u for Saturn – II, 2.1 GeV/u for Bevatron and 4.2 GeV/u for Synchrophasotron. All the three machines are already out of operation.
After the successful demonstration that heavy ions could be accelerated in proton synchrotrons BNL’s AGS and CERN’s SPS machines started ambitious heavy ion programs. In BNL the emphasis was on the acceleration of gold ions up to 9 GeV/u. In CERN the so-called lead program was initiated. The intensity of the accelerated in SPS up to 17.7 GeV/u fully stripped lead ions reached 4.7.109 ions/pulse.
Two synchrotrons specially built for heavy ion acceleration took the baton – SIS-18 in GSI and Nuclotron in JINR. SIS-18 accelerates all ion species up to U73+ to a maximum energy of 1 GeV/u and with beam intensity as high as 4.1010 ions/pulse. Nuclotron is a superconducting machine capable to accelerate ions with Zpr/Apr= 0.5 up to 6 GeV/u.
The story of investigations with relativistic heavy ion beams turned over a new leaf with the commissioning of the heavy ion collider RHIC in BNL. Collisions of gold nuclei at maximum energy 2x100 GeV/u with a peak luminosity L = 1.5.1027 cm-2s-1 were realized.
Principles applied for acceleration of heavy ions are the same as those applied for acceleration of protons. The breakthroughs are related mainly with the invention of the EBIS and ECRIS sources of intensive beams of heavy ions in high charge states, with the invention of RFG accelerator and the progress made in linear injectors and with the invention of electron cooling.
The remaining bound electrons in the multi-electron ions and the high electric charge of the fully stripped (bare) nuclei are the two major factors in which the acceleration of heavy ions differs from the acceleration of protons.
The multicharged ions interact with the molecules and atoms of the residual gas in the vacuum chamber of the accelerator and/or with deliberately set stripping targets. This interactions lead to loss and capture of electrons from/to the projectile electron shell and hence to a jump of the projectile charge to mass ratio. The ion cannot be further guided and focused by the accelerator magnetic structure in a proper way and is lost.
On the other hand ion loss can produce vacuum pressure instability and pressure bumps, which in turn lead to more beam loss. A positive feedback could be established and the beam could be completely destroyed.
The high electric charge eZpr of the fully stripped nuclei compared with the proton charge has many positive and negative consequences. Here are some.
As the particle charge grow up the influence of the adverse space charge effects also increases. The coherent space charge tune shift is proportional to. High space charge tune shift () results in resonance crossing and in beam loss. The intensity limitations are most severe in the booster synchrotron due to the low ion velocity at injection. The cure is to use a large acceptance and to fill this acceptance as densely with particles as possible. A kind of multiturn injection with stacking in both horizontal and vertical phase spaces could be applied. For a small machine like a booster synchrotron the use of large acceptance is cost-reasonable.
The beam rigidity is inversely proportional to the ion charge. Increasing the ion charge you reduce the power necessary for acceleration to a given kinetic energy. On the other hand the less the ion charge the higher space charge limit. Hence a compromise must be worked out.
In heavy ion colliders the beam lifetime is dominated by intrabeam scattering. This leads to particle loss out of the rf buckets and to an increase of the transverse beam emittances. The emittance growth reduces the luminosity. The intrabeam scattering effect scales as .
The paper represents a review of processes which are specific for high energy heavy ion acceleration and which determine to a great extent the achievable parameters and the quality of the accelerated beams.
2. Approaches to acceleration of heavy ions by synchrotrons
The different variants of heavy ion acceleration by synchrotrons are closely related to the available sources of heavy ions.
Three types of heavy ion sources are nowadays in operation – Table 1.
Table 1. Sources of Uranium ions.
Charge state of delivered Uranium ions, Zpr
Beam current, emA
Pulse length, μs
MEVVA – GSI
VENUS – LBNL
EBIS – BNL
ESIS - JINR
Vacuum Arc Ion Sources. These are sources of ions in low charge state, A/Zpr ≤ 65, but with high ion beam intensity, up to 0.25A/Zpr in emA. The achieved in GSI beam currents lie above the space charge limit of the RFQ section. Vacuum arc ion sources are relatively simple. They need neither gyrotron amplifiers nor superconducting magnets. The pulse length is long enough, 500 μs or more, for a kind of multiturn injection into synchrotron to be realized.
Vacuum arc ion sources are widely used in the GSI heavy ion accelerator complex.
The multi casp ion source MUCIS is used for gaseous ions (deuterium, helium, argon, xenon etc.) – . For example Ar1+ beams with 38 emA current were produced.
For metal ions the Metal Vapor Vacuum Arc ion source MEVVA has been developed – . It provides uranium beams with typical total current of 24 emA and the fraction U4+ reaching a rate of 67%. The new modification of MEVVA ion source, named VARIS, can generate even more intensive uranium beams. With arc current 700 A at 30 kW and a careful tuning of the extraction system the analyzed U4+ current has reached 25 emA.
Electron Cyclotron Resonance Ion Source, ECRIS. ECRIS was suggested by R. Geller. It is able to generate high current, medium charge state beams. The ion source operates at dc or long pulses (~200 μs) modes. The latter mode is called “afterglow” mode and deliver larger intensity. The ion sources of ECRIS type are very reliable and stable in operation. The recent improvements are related with raising the RF frequency and the strength of the magnetic field applying a gyrotron amplifier and superconducting solenoidal and hexapole radial cusp magnetic fields.
The developed in LBNL superconducring ECRIS VENUS utilizes a commercially available 10 kW – CW, 28 GHz gyrotron amplifier and has a peak magnetic field of 4 T – . It can produce 240 eμA U30+ or 5 eμA U48+ beams.
Electron Beam Ion Source, EBIS. EBIS produces ion beams in highest available charge states. The ion source was developed in JINR by E. D. Donets. For EBIS the total extracted charge per pulse is independent of the ion species and of the ion charge state. The charge state distribution is narrow. Typically the desired charge state rate is about 20% of the total current. EBIS produces short pulses of high current and is well suited for single turn injection into synchrotrons but not for multirurn injection.
The recent advantages made in BNL have used an electron gun with 10 A electron beam current and a 0.7 m long trap – . A beam of Au32+ ions with 550 eμA in 15 μs pulses has been produced. BNL EBIS could also deliver beams of U30+ ions with intensity 5.109 ions in 10 μs pulses. The time between the successive pulses is 100 ms. This source uses a 5 T superconducting solenoid.
By using of electron reflectors E. D. Donets in JINR succeeded in formation of electron strings with high linear electron space charge density which could be used for effective production of highly charged ion beams. They called this modification of EBIS – Electron String Ion Source, ESIS – . In the first tests with JINR “Krion-2”, converted to ESIS type ion source, Ar16+ beams with current up to 150 eμA in 8 μs pulses have been produced.
To sum up – from the point of view of injection and acceleration in synchrotrons we could distinguish three groups of ion sources – Fig.1.
Sources of single charged ions or of ions in very low charge state, but with highest intensity, which is reached by now.
Sources of medium charged ions with medium beam current.
Sources for ions in highest charge states, which are reached by now, but with low beam current.
Fig. 1. Different types of ion sources. On the horizontal axis the product of
electron density and confinement time is shown On the vertical axis the
electron energy is shown.
Three different approaches to the acceleration of heavy ions by synchrotrons follow from this classification of the sources in a straightforward way.
Variant with a high current, low charge state injector. This approach to the heavy ion acceleration has been developed for many years in GSI – [6,7]. A multicasp ion source for gaseous ions and a metal vapor vacuum arc ion source for metal ions are used. These sources deliver intensive beams of low charged ions.
The first section of the GSI high current linear injector is a 36 MHz, 9.4 m long, RFQ structure, working in H110 mode – . This first section accelerates ions up to 120 keV/u. It is followed by a 20 m long IH drift tube linac. This IH-DTL further accelerates ions to 1.4 MeV/u, an energy that is high enough for a N2 – jet stripper to be applied. The gas stripper raises the ion charge state from U4+ to U28+. Energy 1.4 MeV/u is too low energy and the stripping efficiency is only 12%. This is compensated by the high intensity of the source (15 emA for U4+).
The famous UNILAC then takes the baton. It pushes ions up to 11.4 MeV/u. At this energy a C – foil stripper can be applied. This second stripper raises the ion charge from U28+ to U73+. The reported stripping efficiency is 15%. Energy of 11.4 MeV/u is high enough to guarantee small residual gas loss in the SIS-18 synchrotron.
We could generalize the GSI approach in the following way – Fig. 2.
Fig. 2. Variant with a high current, low charge state injector
The basic idea is the use of an intensive source of ions in low charge state. Acceleration of low charged ions by linear accelerators require high accelerating voltage and as the voltage gain is limited (4.2 MV/m in the GSI IH-DTL) the length of the linac becomes large. The linear injector must be split to two parts with a stripping section between them. In this way you increase the ion charge state at as low energy as this is possible. Large particle loss due to the bad stripping efficiency at low projectile energy is the price you must pay.
As the pulse length of the used ion sources is large (500 – 1000 μs) a multiturn injection into the booster synchrotron with big number of injected turns could be realized.
Variant with source of heavy ions in medium charge states, working in dc mode. The only source of multicharged ions working in dc mode at the moment is ECRIS. The beam current of the state-of-art ion sources of this type is 200 – 400 eμA depending on the ion species and could be doubled in the pulse (afterglow) mode with 200 – 300 μs pulses. This approach to heavy ion acceleration is realized in the LHC lead acceleration chain – [9,10]. CERN’s ECRIS works at 14 GHz and produces beams of Pb27+ ions with 200 eμA beam current.
The much higher charge states of the ions delivered by ECRIS compared with those from vacuum arc ion source allow to drop out the first stripper in Fig. 2 and thus to increase the efficiency almost ten times – Fig. 3.
Fig. 3. Variant with source of heavy ions in medium charge states, working in dc mode.
On the other hand the dc nature of ECRIS allows applying efficient multiturn injection into the booster synchrotron. In CERN Pb program the injection in LEIR covers 35 turns, with 25 effective ones. An original method for combined injection in both transverse and longitudinal phase spaces is used. This method increases the stored intensity 3 to 5 times and simultaneously reduces the beam emittance 3 times. After the multiturn injection is fulfilled the stored beam is cooled down applying the electron cooling method. The cooling time is short – 0.1s. This allows for up to 12 stacking – cooling cycles to be realized.
Variant with injector of heavy ions in high charge states, working in a short pulses mode.The ion source that delivers heavy ions in the highest at the moment charge states is EBIS. EBIS is able to produce highly charged ions of any species. It has the smallest beam emittance.
With ions in high charge states the RFQ and DTL sections are more compact and efficient.
EBIS is a pulsed ion source. The pulses of extracted ions are short, typically about 10 μs. The pulse length is of the order of the booster revolution time and the single turn injection is the natural choice. The repetition rate of EBIS is 1 – 5 Hz. In principle one could repeat the single turn injection several times stacking the particles in the momentum space.
The accelerator chain is schematically shown on Fig. 4.
Fig. 4. Variant with injector of heavy ions in high charge states, working
in a short pulses mode
This approach has been applied to the JINR Synchrophasotron and after its shutdown to the Syncnrophasotron’s successor – the superconducting heavy ion synchrotron Nuclotron – . The developed by E. D. Donets EBIS “Krion-2” can produce for example 8 μs pulses of Ar16+ and Fe24+ ions with beam currents of 200 eμA and 150 eμA respectively. The repetition rate is 1 Hz.
An important step toward higher beam intensity was made recently in BNL. Increasing the electron current in a test EBIS up to 10 A and improving the ion confinement the BNL team succeeded in producing Au35+ beams with 3.109 ions/pulse. This success encouraged the BNL specialists and they have proposed to replace the Tandem injector with a combination of EBIS, RFQ and short linac – .
Meanwhile E. D. Donets started in JINR R&D investigations in a completely new direction. He suggested the so-called reflex mode of EBIS operation. The new source was named Electron String Ion Source or ESIS. The hopes are that with a 12 T superconucting solenoid this source will be able to produce beams of ions with mass number A from 130 to 238, in high charge state Zpr from 0.42 to 0.38, and with high intensity N = 1.1010 – 5.109 ions/pulse. Plans to use ESIS in the injection chain are under way – .
3. Interaction with residual gas and stripping foils
When the ion beam moves in the accelerator the multielectron ions interact with atoms and molecules of the residual gas or with those in solid or gaseous targets, deliberately introduced in their path. These interactions include elastic and inelastic processes: single and multiple Coulomb scattering, processes of electron loss and capture and processes of excitation and ionization of target atoms and molecules. The loss or capture of electrons by fast moving ions results in the change of ion charge and hence leads to beam loss. The multiple Coulomb scattering has as a consequence an increase of transverse emittance. Spending of ion kinetic energy for excitation and ionization of target atoms increases the relative momentum spread.
In this chapter a brief description of all these processes is given.
A. Electron loss. This is a process of loss of electrons in ion-atomic collisions – Fig. 5. The figure of merit is the so-called atomic velocity , where α=1/137 is the fine structure constant. In fact v0 is the velocity of an electron in the first Bohr’s orbit.
Fig. 5. Process of single electron loss in ion-atomic collisions
According to Bohr’s criterion when an ion penetrates through matter it retains only those electrons whose orbital velocity u is grater than the ion velocity v=βc. For hydrogen-like particles with charge of the nuclei eZpr the mean electron orbital velocity is u=Zpr.v0. For such a hydrogen-like ion the electron loss cross section has a maximum for v=u.
When the ionization is due to atoms instead of nuclei the screening of the nuclear charge by the shell electrons leads to smaller ionization cross section.
Let σi,i+1 be the cross section for loss of single electron by a multielectron ion being in charge state i.
The classical Bohr’s formula –  predicts:
( 1 )
where: Zpr is ion atomic number, Zt – target atomic number, v0 – atomic velocity unit, – radius of the first Bohr electron orbit.
This formula is valid for projectile kinetic energy per atomic mass unit Tn, which satisfies the condition:
( 2 )
and for Zt not much larger than Zpr. For uranium ions the condition (2) reads: Tn > 420 MeV/u.
V. S. Nikolaev et al. -  have introduced the following correction factor to the Bohr’s formula:
( 3 )
( 4 )
This formula is valid for for particles with Zprt/√ 2 and for
for ions with Zpr>Zt/√ 2.
There is no satisfactory quantitative theoretical description of the electron loss and capture cross sections. These cross sections depend sharply on the projectile velocity and as well on the atomic numbers of the projectile and target atoms and on ion charge state i.
Also there is lack of sufficient amount of experimental data on ionization cross sections for high energy highly charged states heavy ions.
Most reliable approach to estimate the cross sections is the direct measurement. However it is difficult to measure cross sections before the accelerator is built because you need ion species at the specified energy range. The available data are for the energies reached in heavy ion cyclotrons and in GSI and BNL accelerator complexes.
Analyzing the experimental data B. Franzke has proposed a semiempirical formula for the electron loss cross section by fast ions – , which received big popularity:
( 5 )
where and are the equilibrium charge states of the projectile and target ions and γ and β – the relativistic factors. For the equilibrium charge Franzke used the formula:
( 6 )
A comparison between the experimental data and Franzke’s formula are given on Fig. 6 for 4.66 MeV/u Pb54+ and in Table 1 for 3.5 MeV/u and 6.5 MeV/u U28+ ions.