PAMELA INJECTION LAYOUT M. Aslaninejad, M. Easton, J. Pasternak, J. Pozimski Blackett Lab, Imperial College London

AbstractFor the PAMELA project, the injection layout for protons and carbon 6+ ions is discussed. The injection

system under consideration would consist of a 30 MeV cyclotron for protons and a chain of elements for carbon ions including an ECR ion source, bending magnets and focusing solenoids, an RFQ, an IH/CH structure and a stripping foil. Particle transport simulations for the proton and carbon injector have been carried out using General Particle Tracer (GPT) software.

INTRODUCTIONSeveral different scenarios for the front end of PAMELA have been investigated [1]. Expected injection requirements for proton and carbon 6+ beams into the FFAG rings of PAMELA are approximately 31 and 8 MeV/u energy, respectively. These values are carried over from the design parameters of the second ring in the KST [2] three ring lattice and are also valid for the lattice under investigation [3]. To achieve the same magnetic rigidity and to allow staged building and commissioning with protons, and for the faster switching between ion species, protons and carbons will be produced in separate sources. The carbon particles will be transported from the ion source into a pre-accelerator via a Low Energy Beam Transport (LEBT), accelerated, and from there injected into PAMELA through a Medium Energy Beam Transport (MEBT), where the particles should meet the energy requirements as noted above. Part of the carbon MEBT is shared with protons, which are delivered into the MEBT via a cyclotron. There are two options for pre-accelerating carbon for PAMELA, either accelerating carbon 4+ ions from the ion source and stripping after the pre-accelerator or accelerating carbon 6+ ions all the way from the ion source. For both options a solution has been investigated (see Figure. 1).

Considerations that led to the proposed injector

A 30 MeV proton beam is equivalent to 3.3 MeV/u carbon 4+ and 7.5 MeV/u Carbon 6+ from the perspective of magnetic rigidity. A Linac for carbon and cyclotron for protons seems to be the only effective solution. A common Linac for both is also excluded as a Linac defines a velocity profile for all species. We should also mention that a very short Linac / re-buncher, less than a meter in length, may be required after the cyclotron to adapt the cyclotron beam output into the bunch structure required for the FFAG accelerator and to increase the energy from 30 MeV to 30.97 MeV as required by FFAG lattice design. Also note that a switching dipole will combine the two different beam lines into a single MEBT that would transport the ions up to the injection point into PAMELA. The MEBT also prepares the beam structure to match the FFAG injection requirements so that the loss of current at injection is reduced as much as possible. The pulse electrical currents for carbon as well as protons are calculated in appendix A.In the case of high current proton sources and in our proposal, the ion source is positioned inside the cyclotron and will be delivered with the cyclotron, but care must be taken for carbon sources. Carbon 4 +

sources can produce currents of 200 , but carbon 6+ ion currents are closer to 1 . While the carbon 6+ accelerator would be more compact and efficient and the current could be sufficient for a rapid cycling machine as proposed for PAMELA, in case of technical difficulties, preventing us from reaching a cycling rate of 1 kHz (see Table. A4 in the appendix A), the fall back option under investigation is to use carbon 4+ injection and a stripping foil which will produce a higher peak current of carbon 6+ for injection.

To achieve the beam current design parameter in the nano-Ampere range, possible losses through the rest of the accelerator chain must be strictly avoided. Since the FFAG design requires carbon 6+, carbon 4+ must be stripped to the higher charge state. This is only possible through a stripping foil for sufficiently high energies of carbon 4+. Thus, carbon 4+ ions should be accelerated in the pre-accelerator and then we can increase their charge state to carbon 6+ ions before injecting into FFAG rings.

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Latest lay out for PAMELA

Proposed setup

We need the same magnetic rigidity for protons and carbon 6+ as injected into the FFAG. The planned scenario for injection is illustrated in Figure 1, where a schematic including the LEBT, pre–accelerator and

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MEBT is shown. We propose to use a commercially available proton cyclotron with kinetic energy about 30 MeV, followed by a short Linac for bunching and final injection energy as the first stage. In the second stage, we utilise an electron cyclotron resonance (ECR) ion source to produce 8-10 keV/u carbon 4+ beams. As C4+ is mixed with C3+ and C5+, we have to employ a spectrometer dipole for mass/charge separation. An aperture then can remove C3+ and C5+ ions. We also use an RFQ to accelerate the C4+ up to 400 keV/u and we then put an IH/CH, (Interdigital H mode/ Crossbar H mode structure) Linac for further acceleration. By this point the energy of the C 4+ is about 7.5 MeV/u and if we now use a stripping foil to strip C4+ to C6+ it would meet the FFAG requirements. Note that stripping from 4+ to 6+ at low energies before the RFQ is impossible and even immediately after RFQ where the nominal energy of the beam has reached 400 keV/u is still too inefficient as the beam would get stuck in the foil. Therefore, we should utilize a

Figure 1: Schematic drawing of the beam injection into FFAG in the PAMELA project.

stripping foil after the IH/CH structure where the beam has acquired enough energy to pass the foil and we can get carbon 6+ from carbon 4+ with high efficiency. Alternatively, we can accelerate carbon 6+ ions all the way from the ion source. In this case, we should make use of an aperture to single out carbon 6+ from carbon 3+, 4+ and carbon 5+. No stripping foil would be needed.

OTHER OPTIONSAn extension of the current 30 MeV proton cyclotron is possible, such that it can also accelerate carbon

ions. In this case this multi-particle machine could accelerate carbon 4+ up to 3.3 MeV/u and carbon 6+ up to 7.5 MeV/u. Therefore, the latter case can meet FFAG requirement too as we can inject both proton and carbon 6+ directly from the same cyclotron into FFAG. Of course, it is assumed that this new machine would be able to accelerate all three species. If, for technical deficiency, it could merely accelerate protons and carbon 4+ with 30 and 3.3 MeV/u, respectively, then again we can get the right charge state to carbon 6+ using an immediate stripping foil, but with the same carbon 4+ energy (3.3 MeV/u). This means the energy obtained for FFAG is reduced by a factor of 3.3/7.5. As a result, we would again need a Linac structure to reach the required energy for carbon 6+. On the other hand, if we first accelerate carbon 4+

through the Linac and use a stripping foil at the end, we would get higher efficiency from the stripping foil. But setting the magnetic rigidity of carbon 4+ and carbon 6+ equal to each other, the acceleration is only 4/9 efficient from energy aspect and 2/3 from velocity aspect due to the velocity profile of Linacs, so this option also has some drawbacks. A detailed investigation is needed to find which method optimises the total efficiency, but in any case we inevitably should put it aside as, while protons are directly injected into FFAG from the cyclotron, we have to take a very long path starting from the same cyclotron and reaching the FFAG for carbons.

Alternatively, it might be considered an option to modify the structure of the second FFAG ring to accelerate the proton ions from 70 MeV up to 250 MeV while accelerating carbon 6+ from 17.5 MeV/u up to 68 MeV/u. This results in less resonance crossing. We have considered the idea of a new multi-particle

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cyclotron that would be able to extract 70 MeV alpha particles (24He2+), or equivalently 17.5 per nucleon

helium beam, and is accordingly also able to extract 17.5 MeV/u for 12C6+. If we keep the current parameters of the present lattice, (30 MeV protons and 7.8 MeV carbon 6+), this machine with 70 MeV injection energy for protons and 17.5 MeV/u for carbon 6+ is not a solution to our needs. But if this new machine can also accelerate carbon 4+ with 7.8 MeV/u then we can use a stripping foil immediately after to strip carbon 4+ to carbon 6+ with 7.8 MeV/u which we need according to FFAG design. The real problem with this scenario is that we would need another cyclotron for delivering a 30 MeV proton beam. This means two cyclotrons, one 7.8 MeV/u carbon 4+ (equivalent to a 70 MeV proton machine) and the other a 30 MeV proton machine, which would not be economical.

ION SOURCE BEAM PARAMETERS

We have selected an Electron Cyclotron Resonance Ion Source (ECRIS) for the carbon for its high beam quality and beam current stability. Depending on the injection scheme, a supernanogun type ECR ion source or hypernanogun type can be employed for a multi-turn or a single-turn injection scheme, respectively. For a single-turn injection scheme a supernanogun ECR with a superconducting magnet can alternatively be used [4]. Since PAMELA takes advantage of a high repetition rate of 1000 Hz, therefore, a single-turn injection can be assumed, but a multi-turn injection is not excluded in case the delivered beam from the injector falls short of the requirement. This is in contrast to other FFAG projects like RACCAM, in which due to a lower repetition rate (100 Hz) a multi-turn injection approach has been applied to produce the necessary current.

A typical ECR ion source produces an 8 keV/u beam via an external extracting voltage say ~24 kV. The choice of the extracting voltage results from the requirement imposed by the Child-Longmuir law , which is a proportionality relation between the current density and the extracting voltage in the form

; being the extracting voltage at a distance d from the source, and to avoid

technical difficulties occurring for higher voltage . For the required carbon currents, the limit given by the Child-Longmuir law exceeds the current requirements by more than two orders of magnitude.Thus the total energy is . The voltage again can be calculated as:

. This external voltage would also extract and also with the energies listed in

the Table. 1.

Table. 1

keV keV keV keV

keV/u. keV/u. keV/u. keV/u.

It is clear that Carbon 6+ has higher kinetic energy using the same extracting voltage. Since the energy of the Carbon 6+ particles exceeds those of Carbon 5+ and Carbon 4+, in the phase space plane they show higher values of the longitudinal velocity in one snap shot. (See Figure 2)

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Figure 2: Longitudinal Velocities of Carbon 6+ (top), Carbon 5+ (middle), and Carbon 4+ (bottom), immediately after the Electron Cyclotron Resonance Ion source (ECRIS). Carbon 6+ shows the highest kinetic energy applying the same extracting voltage, here

24 kV, to all species.

Longitudinal and transversal starting conditionsDue to the lack of measured input data for the simulation, and based on the beam energy considerations shown above, an initial particle distribution was produced to represent the beam extracted from the ion source. The following pictures show the particle distributions used as an input for the following simulation.

The initial phase space distributions of the particles, seconds after the release from the ion source are shown in the figures 3 and 4. The distributions consist of 2000 carbon 6+, 1000 carbon 5+ and 1000 carbon 4+ particles.

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Figure 3:Initial horizontal and vertical phase space distributions of the 2000 Carbon 6+ (green) 1000 Carbon 5+ (red) and 1000 Carbon 4+ (blue) particles starting from the ion source at time 10-8 s.

Figure 4. Phase space distribution of 1993 carbon 6+ particles left after the spectrometer dipole.

Histogram of distribution of 1993 carbon 6+ particles left after the spectrometer dipole.

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Typical beam parameters for carbon injection from an ECRIS are shown in the table. 2.

Table. 2.Beam Radius Beam Divergence Beam normalized

EmittancesBeam pulse duration

2 mm 50 mrad 0.25 mm-mrad 506 ns (see appendix A)

Of course, the beam parameters strongly depend on the RFQ acceptance. As a remark we here state that according to the parameters given in the appendix A, the pulse duration amounts to approximately. As we will mention later the design frequency of the RFQ is approximately .

Therefore, the bunch distance inside the RFQ is . If we consider of the RF period for

the acceleration (i.e. out of ), the bunch length would be accordingly. The number

of bunches in the train can be approximately estimated to be .

LEBT

A Low energy beam transport line (LEBT) will be utilized to transport the particles from the source to the RFQ. For carbon, the layout consists of 4 solenoids (Rectangular coils) for transversal focussing and a spectrometer dipole to select the required charge state and remove the others. The particle dynamics of the carbon beam was studied using the General Particle Tracer (GPT) from Pulsar Physics, [5]. At the current

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stage simulations have been done using built-in elements of GPT. It is planned to use a realistic field map for the elements later. Two solenoids each 0.25 m long are positioned at approximately 0.325 and 0.875m from the ion source. The first solenoid runs the particles parallel and the second one focuses them. After the charge to mass separation by the spectrometer, we position two more solenoid to focus the beam into the RFQ. The parameters of the rectangular coils are shown in the table.3

Table.3 Name Rectcoil1 Rectcoil2 Rectcoil3 Rectcoil4Current 57000 Amp turns 40000 Amp turns 48000 Amp turns 105000 Amp turnsInner radius 0.05 m 0.05 m 0.03 m 0.03 mOuter radius 0.10 m 0.10 m 0.08 m 0.08 mWidth 0.25 m 0.25 m 0.25 m 0.25 mDistance from the Ion source

0.325 m 0.875m 0.250 m* 0.750 m*

After the 90 degree spectrometer dipole, a change in the reference system takes place. Therefore, the values characterised by asterisks are the distance with respect to the coordinate system located in the spectrometer.

Figure 5: Trajectories of 2000 C6+ particles from the ECR ion source toward RFQ entrance. Beam bends down because of the spectrometer dipole. Two solenoids before and two after the spectrometer are used to run the beam parallel and focus it.

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The spectrometer dipole bends the beam downward. Different charge states will bend at different radii of curvature in the dipole. The radius of the dipole is 0.25 meters. We may require the beam to enter and exit the dipole normal to the magnet faces. But, due to the weak focusing effect of the dipole, we have a focusing in one plane, but not in the other plane. We should, consequently, introduce an effective edge focusing through the pole face rotation angles at the entrance and at the exit of the dipole. Introducing an edge angle gives rise to a edge focusing effect in the vertical plane, while an edge defocusing effect for the horizontal plane, which reduces the total horizontal focusing. In other word, at the cost of having less horizontal focusing, we now have also a vertical focusing. Angles of incidence and exit pole faces are taken to be 0.25 rad, for both.

An aperture (10 mm in radius) after the spectrometer dipole ensures that only the ions in the necessary charge state are allowed to enter the pre-accelerator. We also need an aperture before the spectrometer dipole (10 mm in radius) to partially remove carbon 4+ and carbon 5+. Without the first aperture the trajectories of Carbon 6+ and carbon 5+ would be quite mixed up so that the second aperture after the dipole would not separate them properly. The final section of the LEBT line may include a chopper for beam injecting into PAMELA, together with two lenses that act, firstly, to ensure that the beam through the chopper is parallel and, secondly, to focus the beam into the RFQ, as the RFQ requires a convergent beam to yield a reasonable transmission.

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Figure 6: Trajectories of 2000 C6+, 1000 C5+ and 1000 C4+ particles from the ECR ion source toward RFQ entrance. A spectrometer dipole bends the beams downward. Different charge states will have different radii of curvature while passing through the spectrometer dipole. An aperture immediately after the spectrometer dipole can remove the unnecessary species, such as C5+ and C4+ beams, as is shown in the figure, and let only the desired species (C6+) through the rest of the linac.

RFQ RFQs use electric fields for both transverse focusing and acceleration. The transverse field is equivalent to magnetic

quadruple field and produces focusing in one transverse dimension and defocusing in the other transverse dimension. As the field oscillates in time and the particles travel down the length of the RFQ, the field produces a net focusing effect in both transverse dimensions. To produce longitudinal acceleration as well as transverse focusing, modulations on the rods or vanes of the RFQ are used to create a longitudinal electric field. Treating the electric field close to the beam axis in the electrostatic approximating, as , the transverse fields have the form

Where is the magnitude of the modulation in the field relative to the standard quadruple field, D is the spatial period of the modulations and is the frequency of the RF. The first term in each expression gives the transverse focusing effect and the second term gives the acceleration effect.

both are linear functions of x and y because they show a quadrupole field, but this quadrupole along the z axis has modulations and becomes narrower and wider. Therefore, there must be a z dependence. On the other hand, as theses modulations are periodic, they are in the form of . For the time dependence there is a dependence.

The field satisfies Laplace’s equation, such that gives

Which, after substituting in Equations for and and integrating , gives the longitudinal field ,

It is clear that the accelerating filed has two terms, one in the z directions and the other in the –z direction.This longitudinal electric field resolves into two travelling waves, one moving against the ion beam and one moving with it(the cause for bunching). The wave moving with the particles will provide an accelerating force for ions in phase, with a synchronous velocity of

coming from

As the synchronous particle is being accelerated, increases with z. To continue the acceleration, the spatial period D of the rod or vane modulations must increase in phase with the synchronous velocity. This is a major parameter in determining the design of the RFQ rods or vanes.

RFQ SIMULATIONA full RFQ design requires optimization of the rod modulations to provide the correct bunching and acceleration for the specific particles and energies to be used for PAMELA. The following simulations are based on the details of the RFQ for the Front-End Test Stand (FETS), and various scaling laws have been investigated to determine the changes required to produce a carbon RFQ. The FETS RFQ uses four vanes, but the lower frequency of the PAMELA RFQ is better suited to a four –rod design.GPT has been used to track carbon ions through a simulated RFQ. The original FETS RFQ is optimized to accelerate a high-current proton beam from 65 keV to 3 MeV. Replacing the proton beam with a carbon beam without modifying the RFQ parameters requires a carbon input beam at 65 keV/u, or a total energy of 780 keV, which is unfeasible from any existing carbon ion source.The magnitude of the electric field also needs to be increased to accelerate the carbon ions. As a carbon 4+ ion has a charge -to-mass ratio a third of that of a proton, the electric field magnitude needs to be increased three-fold (

thus mass/charge matters). We note that the requirement for accelerating different species

in the same RFQ is to have the same charge /mass ratio(even in principle we will be able to accelerate them simultaneously, in alternating cycles of the RF ). For example, using FETS RFQ, we are not able to accelerate carbon 4+

as q/m=1/3, while for proton this ratio is equal t one. Therefore we should increase the electric field 3 times.

Studies using GPT confirmed these results. Simulations shows that acceleration only starts to occur with electric filed magnitude three times larger than that for protons and initial energy of 65 keV/u. In other words, if we do not change the RFQ parameter and keep them as they are designed for the FETS proton RFQ, all we need to do is to increase the electric filed 3 times to be able to accelerate the 65 keV/u carbon. But in practice we have to take a practical approach and accelerate carbons from a different energy.

In that case, we need to change also the other parameters of RFQ in comparison with the current parameters of FETS RFQ.To avoid unreasonably high input energy and field magnitude, the next stage of simulations involved reducing the length of the RFQ and reducing the frequency of the electric filed, scaling the modulation pattern with the length of the RFQ. An operating frequency of 200 MHz was chosen for the ease of production with available RF power sources, and because reducing the frequency (increases????) the Q values of the cavities, thereby reducing the power requirements. The synchrotron velocity of an ion in the RFQ is given by the above equation. The FETS RFQ is designed for protons with an energy of 65 keV, and therefore a synchrotron velocity of because

and thus as therefore,

.

A reasonable energy from available carbon ion sources is 8 keV/u, or total energy of 96 keV, which for carbon 4+ ions can be achieved with a voltage of 24 kV. This corresponds to a velocity , so the carbon RFQ for PAMELA needs a reduction in the synchrotron velocity of a factor of 0.37. Reducing the frequency from 324 MHz to 200 MHz produces a reduction in velocity of a factor of 0.62, so a further factor of 0.60 is needed, which can only be achieved by reducing D. GPT allows transformations of the field map by a fixed factor, so a number of simulations were run, in which the z-axis is compressed by a fixed factor. Compressing the whole z-axis will also reduce D by the same factor. As expected, a factor of 0.6 produced the best acceleration (reaching a final energy of 382 keV/u)with an initial energy of 8 keV/u. This compression factor results in an RFQ length of 2.4 m.The modulation of the rods of the RFQ produce the longitudinal field that enables particle acceleration, but they also affect the transverse field, and act to reduce transverse focusing, Net focusing can still occur as long as the modulations in the eclectic field are not too large in magnitude, requiring

Where is the magnitude of the modulating electric field, a is the distance between the electrodes and the axis and is the phase of the particle relative to the phase of the electric field.

The limit for RF breakdown were investigated experimentally by Killpatric, leading to a formula for the electric breakdown limit now known as the Kilpatric limit :

where d is the smallest gap distance between electrodes , is the mass of a proton and is

the charge of an electron. Often a linear approximation is used to evaluate the Kilpatrick limit:

Which gives a value of 45 kV when using a minimum gap distance of 2.5 mm and a frequency of 200 MHz. The ratio between the Kilpatrick limit and the actual electrode voltage is known as the Kilpatrick factor, and using current technology Kilpatrick factors up to 2.0 are acceptable for an RFQ and this value is likely to increase as research advances. The required voltage of 80 kV corresponds to a Kilpatrick factor of 1.8, so is within achievable limits.

Table: simulation parameter for carbon RFQ modelParameter ValueE-field frequency 200 MHzInitial particle energy 8keV/uRFQ length 2.4 mElectrode potential 80kV

General Scaling rules for an RFQ 1- If mass over charge of two species are the same, then with the same RFQ you can accelerate both, but the

initial and final energy of the particles per nucleon should be the same. There is no need to change the length

and the frequency of the RFQ as long as you do not want to change the initial and final energy of any of the species.

2- If the mass over charge of two species are not the same, you have to have to increase the RFQ electric field f up to the mass over charge for the species having higher ratio of the mass over charge. Again you do not need to change the length or frequency of the RFQ if you the initial and final energy for both species are supposed to be the same.

3- If you want to change the acceptance (initial energy of the particle) energy or final energy (exit energy of the particles from RFQ) of the RFQ, you need to change the length and /or the frequency of the RFQ, even for only one species.

There are two options for pre-accelerating carbon for PAMELA, either accelerating carbon 4+ ions from the ion source and stripping after the pre-accelerator or accelerating carbon 6+ ions all the way from the ion source. We have produced two RFQ designs for these two options. Depending on the achievable rep-rate of PAMELA and consequently the choice of the ion (carbon 4 or 6) for acceleration in the injector, two different RFQ layouts are preferable and described below.The current simulations of the carbon RFQ are based on an existing RFQ design for high-power proton beams, scaled to match the PAMELA parameters. For carbon 4+ ions, the lower frequency of the RFQ favours the rod design [give reference here] as shown in Figure 7.

Figure 7: Shape of rods within RFQ structure

To adjust the RFQ from a high-power proton accelerator to a low-power carbon accelerator, three changes are required. The energy-per-nucleon of the carbon 4+ ions (8 keV/u) is much lower than the proton source (65 keV), as the ions are twelve times heavier. This requires a reduction in the synchronous velocity of the RFQ by a factor of 0.35, which is produced by reducing the frequency from 324 MHz to 200 MHz and reducing the length of the RFQ from 4.1 m to 2.3 m (see Equation 1).

Equation 1: Scaling law for synchronous velocity of the RFQ

Equation 2: Scaling law for field modulation magnitude

The pole-to-pole voltage required is also subject to change to keep the relative magnitude of the modulating field constant (see Equation 2). However, the changes required from the lower charge-to-mass ratio of the carbon ions is partially balanced by the changes required from the lower frequency, producing a net reduction by a factor of 0.88 from 85 kV to 75 kV. The Kilpatrick factor, which quantifies the likelihood of electric breakdown between the poles, is dependent on the voltage and the frequency. The change in this value is also balanced and only increases slightly from 1.63 to 1.65.

These design parameters are summarised in Table 3.

Picture of variation of modulation as a function of the cell number is required.

parametervalue

energy at start of RFQ 8 keV/ufrequency 200 MHz

length 2.3 mpole-to-pole voltage 75 kV

beam current 300 µAbeam divergence -60 mradbeam emittance 0.25 π mm mrad

Table 3: Input parameters for carbon 4+ RFQ simulations

The simulated PAMELA RFQ accelerates carbon 4+ ions from 8 keV/u to 371 keV/u (see Figure 8). The beam current is 300 µA of carbon 4+, which is available from an ECRIS. The simulations have produced a transmission of 98.8% and a final energy spread (rms) of 5 keV/u. The simulation results are summarised in Table 4. Figure 9 shows the path of 1000 macro-particles through the RFQ.

Figure 8: Final energy histogram for carbon 4+ RFQ simulations

Table 4: Output results for carbon 4+ RFQ simulationsresult value

energy at end of RFQ 371 keV/urms energy at end of RFQ 5 keV/u

transmission 98.8%

Figure 9: Paths of macro-particles through the RFQ. Lost particles are shown in colour, with different colours corresponding to losses at different locations in z.

Transversal RFQ output distributions are needed here.

In case of a rapid-cycling FFAG (rep-rate > 500 Hz), the use of carbon 6+ is favourable. This not only has consequence on the rod modulation and resonator set-up, but also a superconducting RFQ must be considered for the following reasons.

The time to fill an RF cavity can be approximated by the inverse of the frequency and the q-value of the cavity (

). For a 200 MHz cavity with a q-value of ~1000, this filling time is of the order of at least 5 µs. The FFAG

ring, on the other hand, has a revolution time of approximately 1 µs, and half-filling the ring at injection (to leave time for kickers etc.) will require ~500 ns pulse. This means that, at injection, we will dissipate power ten times longer than we will produce useful beam.

Converting the RFQ and Linac to a superconducting design allows us to produce a DC beam, giving an effectively infinite filling time. Power losses will go down as the ratio of the q-value, giving a superconducting RFQ five orders of magnitude lower power losses than a standard-conducting RFQ. What would require 50 kW of power for a normal-conducting solution would only require 0.5 W for a superconducting solution, as the peak power of the beam at the end of the RFQ will be in the range of half a Watt; in case of a normal conducting accelerator, nearly all RF power is lost in the walls of the RFQ and the efficiency is very low. The reduction in costs of the RF amplifier should more than cover the increase in cost for the superconducting elements.

Also, as the power requirement is so low, a wide-band RF amplifier can be used, and we can specify the RFQ frequency based on the best particle dynamics, rather than simply by what RF equipment is available. This allows us to easily accommodate carbon 6+ ions as well as carbon 4+ ions.

The design parameters for a superconducting carbon 6+ RFQ are summarised in Table 5.

Table 5: Input parameters for carbon 6+ RFQ simulationsparameter value

energy at start of RFQ 12 keV/ufrequency 240 MHz

length 2.4 mpole-to-pole voltage 78 kV

beam current 1 µAbeam divergence -60 mradbeam emittance 0.25 π mm mrad

These parameters are not the only working point, however, and further optimisation of the design may alter these values, while keeping the net effect of the changes the same.

The increased frequency of the RFQ favours a vane design rather than the rods above. The shape of the vanes is shown in Figure 10.

Figure 10: Shape of vanes within RFQ structure

The Kilpatrick factor for this simulation is virtually unchanged at 1.64. The results of these latest simulations are shown in Table 6 and Figures 11 and 12.

Table 6: Output results for carbon 6+ RFQ simulationsresult value

energy at end of RFQ 557 keV/urms energy at end of RFQ 8 keV/u

transmission 99.2%

Figure 11: Final energy histogram for carbon 6+ RFQ simulations

Figure 12: Paths of macro-particles through the RFQ. Lost particles are shown in colour, with different colours corresponding to losses at different locations in z.

These very promising preliminary results have been achieved without optimisation of the RFQ modulation parameters specific to PAMELA, so we are very confident that these results can be improved. The final solution will also depend on the RFQ frequency choice for the PAMELA ring. Also, the final energy of the RFQ can be adjusted by adding or removing acceleration cells, which is not possible when scaling an existing design, but is straightforward when optimising a new design. The optimal final energy depends on the design of the IH/CH Linac, and has therefore not yet been defined for the RFQ. Once the simulations for the LEBT are complete, RFQ simulations can be run using the output distribution of the LEBT, rather than using the current idealised starting conditions.

Transversal RFQ output distributions are need here again. Linacs-IH/CH structures

In general, the advantage of using a linac as the injector is the high current limit of such accelerators and the good transmission due to strong transversal focusing. The main disadvantages are high investment costs and large space requirements. While the current limit exceeds the requirement for medical applications by at least a factor of ten the achievable average electric field strength for acceleration of low beta ion beams is usually 3 MV/m. While this excludes hadrons Linacs for medical applications, the high current available at low energies (1-5 MeV/u) makes them ideal candidates as an injector. A typical structure to use at the low energy end would be an RFQ accelerating the ions to approximately 400 keV/u offering superior transversal focusing and high beam transmission followed by a DTL structure (IH/CH, Spokes) which offers a higher acceleration rate (average longitudinal fields) compared to RFQs at medium energies. The RFQ offers a high beam current. All available external ion sources can be used. One RFQ can be used for all species exceeding the design charge over mass ratio, it will be cheaper for different species and offers the opportunity to start with a low power RF source for driving the RFQ and upgrade for smaller charge over mass ratio by increasing the RF power (factor 9 for Carbon 4+).Interdigital H structure is a type of drift tube Linac where the drift tubes are not mounted on one side, but on both alternating sides so that they look like the fingers of the two hands sticking into each other. It uses a different H mode than conventional DTL, which makes them smaller for low frequency systems. On the other hand, in Crossbar H structure (CH), Interdigital fingers are rotated by 90 degrees which again reduces the size even further. The magnetic field distribution is like in a 4 vane RFQ so that the flux is in the 4 quadrants. H-mode accelerating structures or transverse-electric (TE) - mode structures, are structures with a predominant RF longitudinal magnetic field, especially in the outer regions of the cavity [7]. The RF electric field is concentrated in the cavity inner regions, and would be transverse to the cavity axis in a simple pillbox cavity. But, an effect of the drift tube loading is to produce a longitudinal electric-field component near the beam axis as necessary for acceleration of the beam. As the beam propagates along the beam axis, it sees the structure as operating in an effective mode [7]. The IH mode may be considered like a TE110 of a pillbox cavity, while the CH mode is similar to a TE 210 pillbox cavity mode. Both H-mode structures have very high

shunt impedance which results in high RF power efficiency compared with the Alvarez DTL. Very compact drift tubes resulting in very small capacitance and the enhanced transit-time factor from mode operation contribute to the high shunt impedance. On the basis of the shunt impedance, the IH structure is better for velocities below about =0.1, whereas the CH structure is better for velocities in the range of about =0.1 to =0.5 [7].As the efficiency decreases with velocity, RFQ would not properly work in acceleration to 7 MeV/u which seems in the moment to be the energy we need to inject into FFAG. On the other hand, at 200 MHz a conventional DTL will be pretty large so IH/CH is most likely choice.Contrary to an RFQ, in an IH Linac, there is no radial focusing. Therefore, a focusing system must be prepared. Quadrupoles between adjacent resonant cavities which includes the IH drift tubes provide the charge particles focusing system.

MEBT

A switching dipole will combine the two different beam lines into a single MEBT that would transport the ions up to the injection point into PAMELA. The MEBT also prepares the beam structure to match the FFAG injection requirements so that the loss of current at injection is reduced as much as possible.

The switching dipole will bend the carbon and the proton beams with different angles, according to the ratio of the magnetic field integral and the magnetic rigidity.

The magnetic rigidity of carbon and proton for PAMELA should be the same. The length of the SD should also be kept fixed. But, depending on the different magnetic fields that the SD should present for carbon and protons, they will bend at different angles so that they both enter the same beam line after the SD. For 31 MeV proton beam the equivalent magnetic rigidity would approximately be .

Injection ScenariosFor injecting protons into the FFAG, different scenarios have been considered. In one scenario, a

vertical injection is considered. The cyclotron and the proton beam line before the SD should be positioned lower than the FFAG. Using a vertical dipole after the SD the beam can be oriented towards the FFAG, which median plane is located higher than the cyclotron one. . Using another vertical dipole and also the septum the beam can be injected into the ring. The latter two elements would also counteract the vertical dispersion produced by the former vertical dipole. In this scenario it is clear that several sets of quadrupoles, would be needed in order to introduce the vertical dispersion matching to zero after injection into the FFAG ring. This requires the phase advance close to 2π between the first vertical dipole and the septum and makes this matching section relatively long. In the second scenario, the FFAG and the cyclotron will be located on the same platform. The beam after the SD can cross the FFAG ring from outside through one straight section (i.e. ring pipe). Now the beam from inside of the FFAG can be horizontally injected into the ring. Note that contrary to the conventional synchrotrons, because of the orbit excursions in FFAGs, the beam injection into the ring should be performed from inside of the ring. In figure 3, we have shown one MEBT layout, in which the cyclotron is located inside the FFAG ring.

Figure 3: MEBT injection layout for PAMELA, based on a cyclotron inside the FFAG ring.

Principles of the MEBT DesignProton beam requirements are summarized in Appendix A. As noted earlier, a switching dipole is

needed to combine the proton and carbon beam lines. The dipole gives rise to an extra dispersion and one needs bending magnets to compensate the dispersion. In order to obtain enough flexibility in performing matching of optical functions, 8 quadrupole magnets are needed - 4 located downstream and 4 upstream the switching dipole. Long drift section is introduced in the common proton/carbon part of the MEBT, where the potential chopper could be located.

Horizontal dispersion matching is realised by choosing the phase advance between SD and the septum. As the exact value of dispersion function at extraction from the cyclotron is not known at the time of preparing this paper zero value was assumed, but this system should have enough degrees of freedom to match other values. As the MEBT is designed such that only the magnetic field in the switching dipole will be changed, when the proton/carbon operation modes will be flipped, the dispersion matching in the carbon line requires additional bending magnet. This is dictated by different deflection angles of the SD for proton and carbon beams. Separate set of quadrupoles are used to perform the beam matching from the linac: 4 quadrupoles upstream the matching dipole and 6 quadrupole magnets separated into 2 triplets between the dipole and the switching dipole. In order to obtain sufficient room in case of locating the cyclotron inside the FFAG avoiding the superposition of magnetic fields of FFAG magnets with the cyclotron, the bending angle of the SD needs to be quite large (about 60 degree). This will produce substantial dispersion, which needs to matched to the value in the FFAG ring.

MADX InvestigationFor the layout shown in Fig. 3, the Madx investigation has resulted in the following optical

functions for the proton beam line shown in Fig. 4.

Figure 4: Beta functions and dispersion for the proton line shown in figure 3. The optics is shown in the inverse configuration, which

means that the cyclotron is located on the right and the FFAG cells are located on the left.

The betatron functions in the proton operation mode are shown in Fig. 4. Please note, that the inverse matching problem is presented with the FFAG cells located on the left and the matching cell to the cyclotron is located on the right. Between the 30 MeV cyclotrons and the FFAG we consider a focusing system consisting of usual quadrupoles. From the left, shown is the two PAMELA triplet cells. Each magnet in the cell is a combined function magnet. Triplets are separated by drift lengths, where one meter sbend septum and a one meter rbend kicker at the entrance of the FFAG are located. In this layout, we have considered 4 quadrupoles after and another four before the switching dipole. Each quadrupole is 0.25 meter long. Using the above chain of elements, a matched solution between the cyclotron and the FFAG has been obtained.

In figure 5, we have shown the MADX calculation for beta functions and the dispersions for the carbon beam transport from the linac to the FFAG ring (again in the inverse direction). The line upstream of the SD consists of two quadrupole triplets followed by the matching dipole and the 4 quadrupoles to give enough flexibility in order to match the linac beam.

Figure 5. Horizontal and vertical betatron functions in the carbon line obtained via MADX (again in the inverse order)

Single versus Multi-turn Injection and Linac considerationsOne important issue for beam injection into Pamela is the multi-turn against single-turn injection

choice.Although the high repetition rate (1000 Hz), for Pamela favours a single –turn injection, the low carbon 6+ current from the ion sources suggests to consider the multi-turn injection scheme. In the latter we would need magnetic and electric septum elements and also bumpers instead of the usual kicker used in the single turn injection scheme.In order to adapt the time structure of the beam extracted from the cyclotron to the time structure required for FFAG injection, a buncher might be additionally positioned in the MEBT. The carbon pre-acceleration using an RFQ is discussed in [4]. We also need an Interdigital H/ Cross bar H structure to accelerate the carbon up to the design requirements.

CONCLUSIONS The flexible design of the MEBT to serve for beam delivery in both proton and carbon operation modes was obtained. The only parameters, which needs to be adjusted is the magnetic field in the switching dipole, which would allow for a very short down time during treatment. The beam dynamics studies and final optimisation will be addressed in the future studies.

REFERENCES[1] M. Aslaninejad et al., Proceedings of PAC09, Vancouver, BC, CA, MO6RFP029,(2009).[2] K. Peach et al., Proceedings of PAC09, Vancouver, BC, CA, TH4GAC03,(2009).[3] M. Aslaninejad et al., “Injection of Proton and Carbon 6+ into the Non-scaling FFAG”, these proceedings.

1- The idea of 70 MeV/u Cyclotron is still on the table, but, there is not much hope for that.2- Parameters of 30 MeV proton cyclotron machine recently have been received from IBA through a confidentiality agreement. Therefore, a new simulation with these new parameters should be done.3-Space Charge effects must be taken into account..4-Work on the RFQ in progress.5-IH/CH structure yet to be investigated.

APENDIX ACalculation of total pulse electric current for Carbon 6+ and Proton.

The radius of PAMELA is, approximately, equal to .The objective kinetic energy of carbon 6+ at the injection into the FFAG amounts to 7.902 MeV/u. Therefore the rest and total energy would be MeV and

=11272MeV.

Accordingly, we can write at injection into

the FFAG. We obtain the velocity according to the Table. A1

Table.A1Radius of the ring Circumference Relativistic beta at

Injection Corresponding velocity at injection

The revolution and the pulse time can be obtained as listed in Table. A2Table.A2Revolution time Pulse time

Note that as nearly half of the revolution time should be allocated to the kickers and to

fill the FFAG, we consider pulse time to be as .

Since the harmonic number is assumed to be , therefore, RF period must be of

the . The parameters are listed in the Table. A3

Table.A3Harmonic number RF period RF frequency

For PAMELA, we need particle (carbon 6+) per second for treatment. The repetition rate of FFAG is assumed to be .

This means that we have injection 1000 times in a second. Each cycle lasts 1 ms. In other words, we inject particle in each cycle. To illustrate this further we can do a simple comparison in Table A4 for machines with different repetition rates to see the currents needed per one cycle

Table.A4Repetition Rate Hz 200 Hz 50 Hz 1 HzIon Per Cycle

This is the pulse particle current during one pulse duration within each cycle. But, the pulse duration within each cycle, as mentioned above, is ,

thus, the pulse particle current becomes, particle per second.

Parameters are given in the Table.A5.

Table.A5Repetition rate Duration of

each cycleInjected particles in each cycle

Pulse particle current

particle/second

Put it in another way, we would say the duty factor is

and, therefore, s.

Note 1: As , for and we obtain ,

therefore, as a general rule, the relation between the electric and particle current reads

particle current.

Therefore, pulse electrical current would be particle

currentFor carbon 6+, we should multiply this by charge state; electric current. Parameters are summarized in the Table.A6.

Table.A6

pulse particle currentPulse electrical current Total pulse electrical current for

carbon 6+

For proton we should do the same calculations. The results are shown in the Table.A7.

Table.A7Radius of the ringCircumferenceRelativistic beta at InjectionCorresponding velocity at injectionRevolution time

Pulse time

Harmonic numberRF period

RF frequency

particle/secondRepetition rate

Duration of each cycleInjected particles in each cycle

Pulse particle current

pulse particle current

Pulse electrical current

Note that betas arebetas are for injection. For extraction we can follow the above approach to find the RF frequencies. For example ,example, extraction beta for proton from the first ring is about (~0.614), therefore trev=C/(beta*c), trev=39.276/(0.614*3e8) =2.1322e-007and trf=trev/h, trf=2.1322e-007/10=2.1322e-008And finally we have frf=1/trf=4.6899e+007~46.9 MHz.

Here we can define the frequency swing (frequency ratio):46.9/19=2.468

Note also that we can raise question about the harmonic number 17. It seems that if we had chosen harmonic number 19 in the first ring then both proton and carbon would have had equal RF frequency for the injection, but then we would have had a problem for the equality at the extraction.

REFERENCES[1] K. Peach et al., Proceedings of PAC 2007, p. 2880.[2] E. Keil, A. M. Sessler and D.Trbojevic, Phys. Rev. ST Accel. Beams 10, 054701(2007).[3] K. Peach et al., “PAMELA overview: design goals and principles”, TH4GAC03, these proceedings.[4]B. Schlitt, U. Ratzinger ,”Design of a carbon injector for a medical accelerator complex”, EPAC 1998.[5] http://www.pulsar.nl/gpt. [6] M. J. Easton et al., “RFQ design optimization for PAMELA injector”, FR5REP066, these proceedings.[7] T. P. Wangler, “RF Linear Accelerator”, 2008 WILEY-VCH Verlag GmbH & Co. KGaA Weinheim.