RF for cyclotrons

P.K. Sigg Paul Scherrer Institute (PSI), Villigen , Switzerland

Abstract The following paper will give an overview of cyclotron-specific RF design: it will deal with classical RF structures (Dees), which are mostly based on a λ/4 or λ/2 coaxial line design, and extend to cavity concepts deviating from conventional cyclotron resonators. Such cavities usually can only be employed in Separated Sector Cyclotrons (SSCs), because their designs ask for more space for the RF cavities. Modelling methods, mechanical design and some results are also presented. Specific characteristics and requirements for RF power amplifiers are introduced; illustrated by two types of power amplifiers. Finally, basic concepts and prerequisites for control systems are presented.

1 Introduction As has previously been noted in references on cyclotron cavities [1], cyclotrons have been around for quite a while and have evolved into numerous different types — for a large variety of applications. Cyclotrons started out as purely experimental machines, used in nuclear- and atomic physics, later in applied physics, but now also include such exotic ‘species’ as high-energy heavy-ion accelerators for research (radioactive beams), high-power proton cyclotron applications (HPPA), used for neutron spallation sources and, in the future, possibly for applications like accelerator driven nuclear systems (ADS) for transmutation [2] or in energy amplifiers [3]. With respect to high-power accelerators, it should be pointed out that one of the operational accelerators with the highest beam power output in the world — about 1.2 MW (CW) — happens to be a cyclotron [4]. About 80 of these individually designed machines are in operation at the present time. Some other types of cyclotrons, designed especially for medical applications, (like radioisotope production, as well as particle beam radiotherapy), are available as commercial units, and have reached a very high level of reliability, expressed in availability rates in excess of 95%. At present, there are approximately 160 ‘commercial’ cyclotrons in operation worldwide.

For future applications of cyclotrons, availability and reliability become even more important issues. If one analyses reliability data, it becomes obvious that RF systems at present account for approximately 1/3 of all unscheduled beam interruptions in a cyclotron (PSI) [6] as well as in a linac (LANL) [5]. Therefore, designing RF systems and cavities for cyclotrons now will also have to take into account such things as: cavity voltage spark rate, repairability and maintainability. These aspects become paramount if cyclotrons are to be used in ADS systems [7], for example for radioactive waste transmutation [2]. There, only a few unscheduled beam interruptions per month seem to be tolerable at the moment, but this ‘trip tolerance number’ seems to depend heavily on the duration of the beam trips. The PSI two-stage facility at present produces about 20 beam trips per day, of > 1 min. duration. However, all RF systems together are responsible for less than one trip/day!

Since cyclotrons are inherently compact and can be designed for a relatively high efficiency rate (beam power/AC-grid power), they promise to become economical alternatives in future HPPA applications. Such machines would almost inevitably be of the SSC design and will require acceleration cavities capable of very high acceleration voltages (> 1 MVpeak). The cavities tend to be rather large, and thus will operate at relatively low frequencies (in the range of ∼ 20 to 170 MHz), but

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in return, will yield high Q- and Rp- values. The following sections will introduce some of the aspects and practical considerations in the design of cyclotrons.

2 The cyclotron: definitions, components, RF systems

2.1 What is a cyclotron?

It is a circular particle accelerator, based on the following concept:

– Fmag = qv × B is the magnetic force acting on a charged particle, moving inside a magneto-static field B; with q = particle charge; and

– Fcent = – (mv2/r)n is the centripetal force, where m equals the particle mass, and n is ⊥ to the trajectory.

These forces equalized, yield

p RFq B vm r

ω ω= = =

the resonance condition for a closed orbit.

⇒ For a given particle and energy, the RF frequency is fixed and constant.

What are the main components of a cyclotron? (and where is the RF system?)

Fig. 1: A simplified cross-section and plan view of a ‘classical’ cyclotron

El.-static Deflector

RF generator

Vacuum pump port

Beam exit port Vacuum chamber

'Dees' Acceleration gap

Ion source

RF 'Dees' Vacuum chamber

Magnet yoke

Magnet coils

Magnet coils

Ion source

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At particle energies higher than a few MeV, however, m = m0 no longer holds, and so, to compensate for the increasing mass (causing loss of isochronism), B was increased with radius. This however, results in axial defocusing. To compensate for that effect, the so-called ‘flutter’ is introduced. It consists of adding a suitable azimuthal modulation to the magnetic field, to compensate for the axial defocussing effect of the radially increasing B. Such a machine is called an ‘Azimuthally Varying Field Isochronous Cyclotron’, or AVF isochronous cyclotron.

Over 200 cyclotrons have been built, to accelerate almost every type of particle; from protons to uranium, to energies from a few MeV to 1 GeV. Recently, the range has been extended to include radioactive particles, as well.

2.2 Pole shapes, effects on RF system design

Fig. 2: Different pole shapes (for ‘flutter’) for AVF isochronous cyclotrons

The choice of the pole shape and the number of sectors have a great impact on the available space for RF systems. Dees, and possibly stems and liners have to fit into the gaps and/or valley sections.

In order to reach a high Q-value (and therefore low losses) for a desired Dee voltage, RF designers would like to have a maximum of space available. (Ideal: ⇒ Separated sector cyclotron!)

2.3 ‘Classical’ λ/4 cyclotron resonators and Dees

Fig. 3: Different types of λ/4 coaxial cyclotron resonators, plan view and cross-section

Three spiral sectors

valley valley

valley hill

hill hill

Dee with glass feed-trough and external inductor for tuning of the resonance frequency (antique!) Two λ/4 lines, with one movable shorting plate, for frequency tuning

Two separate coaxial λ/4 lines, movable shorts for frequency tuning Single λ/4 coaxial line with a ‘Dummy Dee’; movable short for frequency tuning Side view

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The original cyclotron had electrodes resembling the letter ‘D’, and this name stuck, even though the original shape is now only rarely used. In all classical cyclotrons, the Dees are (capacitive) electrodes, inserted into the magnet gap, usually in the ‘valley’ of the pole plates. A shorted coaxial part (the inductive end) extends to the outside of the magnet yoke, thus completing the structures to λ/4 resonators.

2.4 Examples of cyclotron RF designs

Many variations of the ‘classical’ solution are possible, an extreme case being the TRIUMF cyclotron. – More than one Dee (2–4), to increase the energy gain per turn (Fig. 5). – Each Dee connected to an upper and lower coaxial λ/4 section, to form a vertical λ/2 resonator – Two Dees, coupled directly or capacitively in the centre, forming a horizontal λ/2 resonator

Fig 4: ‘Classical’ cyclotron with one λ/4 Dee (coaxial resonator), and panel tuning (Texas A & M)

Fig. 5: A more recent design: the NSCL superconducting cyclotron. It uses three Dees with a λ/2

coaxial resonator design, vertically protruding through magnet and vacuum chamber.

Panels for frequency tuning

The ‘Dee’

Capacitive trimmer

Amplifier

λ/4

λ/2 Dee

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3 Special conditions for high beam power cyclotron RF systems When accelerating high (mA) beam currents in cyclotrons to higher energies, new problems arise, and ask for solutions. To reach higher beam energies (say > 120 MeV) at high beam currents, multi-stage cyclotron arrangements are usually employed, with the final (high power) cyclotron stage being of ‘pure’ separated sector design, of the type usually called a ‘ring cyclotron’ (see Fig. 6). These machines do have sufficient space available in the centre to make a different type of RF cavity design feasible; the ‘single-gap cavity’. Such cavities are basically waveguides, operating in fundamental mode, with a sinusoidal voltage distribution along the acceleration gap. An extension of this ring cyclotron concept can employ superconducting magnet sectors (RIKEN, RIBF) [8], or even include superconducting magnets and cavities, like the TRITRON machine [9].

Generally, the required low extraction losses (< 0.02 %) will call for single turn extraction, that is: high energy gain per turn plus very limited beam phase acceptance (a few degrees) at injection.

To improve the phase acceptance range in a final cyclotron stage, systems with one or more flat-topping cavities and beam-power absorption devices will have to be included in such a design. Flat-topping, that is: adding a third harmonic cavity (operating 180° out of phase — in the deceleration mode) widens the phase acceptance angle for the particle bunches to approximately 25°.

In acceleration cavities, beam power compared to cavity losses, is no longer negligible; the load impedance of the cavity varies widely as a function of the beam load, and either variable couplers for impedance matching, or final power amplifiers that can handle the load variation have to be designed. In the PSI ring cyclotron cavities, for example, beam power is now at the same level as cavity losses; that is: about 300 kW (CW) for each.

In the case of flat-topping cavities, the beam loading effect is even more pronounced: the beam actually deposits energy in the cavity (since the particle bunches are 180° out of phase), acting like a second generator on the cavity, in parallel to the final amplifier. This power can exceed the wall losses in the cavity, that is: in order to maintain the very stringent cavity voltage- and phase control, the amplifier has to either go into an absorbing mode, or an additional load (variable or fixed) has to be connected to the cavity to absorb the excess power [10]. This is one way to reduce the Q-value of the cavity, and of course requires largely overrated RF final amplifiers [11].

Beam injection

Beam extraction

Fig. 6: A typical Separated Sector Cyclotron (SSC). Median plane view (left), and photo (right) of the PSI ring cyclotron (eight sector magnets and four acceleration cavities are visible).

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It is preferable for large SSCs — because of the activation caused by high beam intensity and energy — require that all amplifiers be removed from the accelerator vault. This requires long, tuned transmission lines (l = n ∗ λ) between final amplifiers and cavities, but in turn, allows easy amplifier access and repair, and therefore increases maintainability and availability of the RF system. Ultimately, this concept also reduces the amount of activated material (radioactive waste) produced.

4 Separated Sector Cyclotron (SSC) cavities

4.1 Tools for electromagnetic cavity design

The evolution of cavity design programs and experience gathered with some of these codes has been discussed in Ref. [12]. Most conventional RF resonators in today's classical cyclotrons have been designed using iterative methods, with transmission line element models combined with network simulation techniques (SPICE, etc.), and then building and measuring (scaled) models [1]. For second order optimization of critical regions (e.g., vacuum feed-through of resonator, couplers or tuning devices) and comparison to model measurements, 2D codes (SUPERFISH, URMEL, etc.) were used, due to cylindrical nature of many such elements. Only very simple geometries, like for example the PSI-ring cyclotron cavity, have ever been designed using purely analytical methods the field equations for a simple box in H101 mode (cf. Eq. 1).

As soon as more demanding cavity shapes are involved, however, 3D programs (or extensive model building!) are the only way to optimize cavity designs for

– maximum shunt impedance (Rp) at the fundamental mode; and therefore, minimal RF power losses,

– surface current distribution for cooling system layout,

– multipactor suppression by choice of a suitable geometry (besides proper choice of surface material or coating, of course),

– optimal damping of parasitic modes.

4.2 3D electromagnetic field modelling

Recently, computers became powerful enough to permit 3D electromagnetic field modelling of complex shapes (like Dees!) with large numbers of mesh points (> 1M tetrahedral elements, 2nd order elements). Simulation tools (e.g., MWS, HFSS) have also been greatly refined and improved.

A practical example: A calculation of eigenmodes with ‘Omega3P’ (SLAC), solving for 20 modes, for the PSI RF system including the vacuum chamber, took 45 min., with 32 CPUs on an IBM-SP4. Total memory requirement was approximately 120 GB. For the first time, previously measured parasitic cyclotron modes could thus be numerically confirmed. Details can be found in Ref. [13].

Beam-cavity interactions can also be investigated; the excitation of higher order modes in cavities and vacuum chambers can be analysed and verified [13].

Previously, integrated cavity design (vacuum chamber and cavity as one unit) was rather tedious, because the effects of mechanical forces and thermal effects on the RF geometry were very difficult to predict with reasonable accuracy. Today, mechanical cavity design can be performed using FEA (finite element analysis) simulation. The RF geometry data (from modal simulation) is transferred into a thermal and structural model (mech. simulation method, e.g., ANSYS), taking into account atmospheric pressure and thermal effects [14], [15]. This procedure yields a deformed RF geometry, which represents the operating geometry.

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Mesh of RF cavities and vacuum chamber, created with tetrahedral elements, using CUBIT (Sandia Lab)

1.2 M 2nd order elements, 6.9 M degrees of freedom

Fig. 7: 3D field model of the PSI separated sector RF systems and the vacuum chamber

Measured spectrum (Network analyser data)

Fig. 8: Parasitic cyclotron modes, calculated and measured

4.3 Example of an integrated cavity: the mechanical design

(Illustrated on a 50 MHz cyclotron cavity replacement for the PSI ring cyclotron) – We use: FEA–Simulation (ANSYS in our case) to answer the following questions:

Inner dimensions of the cavity under vacuum ⇒ resonance frequency

Frequency drift (thermal, atmospheric pressure)

Temperature distribution

Frequency tuning range

Effect of manufacturing tolerances

?

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– Applying Sequential Coupled Field Analysis, we arrive at crucial values for:

Inner dimensions of the cavity in air ⇒ essential for manufacturing!

Frequency drift (tuning system)

H- and E- field distribution ⇒ acceleration gap voltage profile

Resonance frequency in air

Q-value

The cavity was designed with a copper inner skin, and an outer stainless steel support structure. The cooling channels (see Fig. 11) are TIG welded onto the copper skin. Hydraulic bellows operate clamps (tuning yokes) for resonance tuning of the cavity — the tuning range and manufacturing accuracy can also be seen in Fig. 11 [17].

Fig. 9: The cavity design procedure in some detail

RF- simulation (Modal)

– undeformed RF geometry

Thermal simulation

– heat flux

– forced convection (cooling)

– natural convection/ambient temperature)

Structural simulation

– results from thermal simulation

– atmospheric pressure

– hydraulic tuning forces

RF simulation (Modal)

– deformed RF geometry

– H- and E- field

– Resonance frequency

– Q-value

– Temperature distribution

– Deformation

– Stress factors

– Frequency drift

– H- and E- field

– Resonance frequency

– Q- value

!

Sequential Coupled Field Analysis

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Fig. 10: The two different models used for the RF field simulation and the mechanical/thermal simulation (1/8th sector)

Frequency tuning range: predicted and measured Calculated and measured key parameters

Fig. 11: Final result: the new integrated cavity for the PSI ring cyclotron

1. RF-Model 2. Mechanical/Thermal Model

20 Node Brick Element (HF120) 85 423 Nodes 18 954 Elements

Resonance frequency Q-value Calculated Measured Calculated Measured

51.040 MHz 50.993 MHz 46 054 45 090

24 hr. commissioning test results: Cavity voltage (MV) Cavity power (kW)

8 Node Brick Element (Solid45/Solid70) 334 205 Nodes 292 484 Elements

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4.4 RF structures for Separated Sector Cyclotrons (SSCs)

Higher energy levels, and/or higher beam power ask for a different approach to cyclotron design:

– New challenges for cyclotrons; existing and new machines:

– Higher energy: 1 GeV or higher; with multitude of particles and charge states → Radioactive beam facilities, e.g., RIBF, at RIKEN (J) [8];

– High beam currents: > 3 mA (p), CW; → (PSI upgrade);

– Very high beam power: > 1 MW, for neutron spallation sources: (PSI at present: 1.2 MW, CW) → MYRRHA project; and in the future: HPPAs for ADS, like for transmutation or energy amplifier projects;

– Superconducting magnets (RIKEN, RIBF), and even superconducting cavities (TRITRON)!

4.5 Classes of SSC cavity designs

The different cavity designs depend on the specifications and geometric layout of a cyclotron, and can therefore be grouped and differentiated by the electromagnetic and geometrical properties:

– Frequency range required:

a) Fixed frequency cavities, used for example in fixed energy proton accelerators, e.g., for spalla-tion neutron sources and ADS. Such designs tend to be simpler and therefore cheaper.

b) Variable energy (and variable particle type) machines: they require cavities with a wide frequency tuning range, in many cases exceeding a frequency ratio of 2:1, and also operate at varying acceleration voltages.

– Single-gap and double-gap cavities

– Cavities can further be separated into: normal conducting and superconducting cavities; up until today however, only one superconducting cavity design has been demonstrated to work in an actual cyclotron, and it differs radically from other well-known designs [9].

4.6 Single-gap vs. double-gap cavities

SSC cavities can be separated into

4.6.1 Double-gap (λ/4 or λ/2 transmission line type) resonators, also called ‘delta’ resonators

They are suitable for applications where a special radial voltage profile (along the acceleration gaps) is desired. Large radial and vertical dimensions of the resonator are possible (for higher energy cyclotron applications); and to obtain high Rp values (with minimal RF power demand for maximum acceleration voltage), the resonator can be made wide at outer radii (piece-of-pie shape).

If the coaxial part of the resonator is not of a simple, cylindrical shape (like in superconducting cyclotrons of the Milan [1] or NSCL [1] design), which can be successfully optimized by 2D geometry codes, but rather look like the GANIL or PSI injector cyclotron RF cavities, an optimal stem design (possibly multiple stems) will be nontrivial, several iterations of modelling might be needed, and are best carried out with advanced 3D RF design tools such as MAFIA [12].

Take the cyclotron apart: Separate sectors for RF cavities and magnets → SSC

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T P T

T: frequency tuners P: RF - power coupler (capacitive)

Cut plane

→

Cut plane →

Vertical cut view

λ/2

Fig. 12: Typical λ/2 double-gap cavity; capacitive fine tuning (T) and capacitive power coupler (P)

Practical experience indicate that the peak RF voltage (< 400 kVp per gap) and Rp obtainable in a large, double gap design will still be somewhat lower than in optimized single gap cavities. An advantage worth mentioning: the fact that a double gap cavity has an inner conductor (coaxial design) means that it is possible to choose between capacitive and inductive power coupling.

4.6.2 Single-gap, waveguide-type resonators

This is a much rarer design, and it has several features which are different from ‘conventional’ double gap cavities. For the simplest, box-shaped design (like the old PSI ring cyclotron cavity) an analytical solution for the electromagnetic field distribution does exist (H101 = TE110 mode):

0

0

0

sin sin

sin cos2

cos sin2

y

x

z

x zE Ea d

E x zH jz d a d

E x zH jz a a d

π π

λ π π

λ π π

⋅ ⋅= ⋅ ⋅

⋅ ⋅= − ⋅ ⋅ ⋅ ⋅⋅

⋅ ⋅= ⋅ ⋅ ⋅ ⋅⋅

(1)

Fig. 13: Basic cavity shape and frame of reference

and, for the wavelength λ at the fundamental frequency f101, we have:

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2101 101 2 21012

2 2

2 1 1; : 21 1

c cand fa d

a d

λλ

= = = ⋅ ++

. (2)

It becomes clear that the width of the cavity has no influence on the fundamental resonance frequency, so a single gap cavity can be made very narrow in the beam plane dimension, where space restrictions are the most severe. It is advantageous to make the cavity narrow along the acceleration gap; and it is preferable to internal electrodes, because such electrodes inevitably increase RF losses and lower the achievable Rp.

Characteristically, higher Q values are obtainable than with conventional transmission line/Dee designs, where acceleration voltages rarely exceed 200 kV and Q values stay below ≈ 20 000.

For comparison: the existing PSI cavities: (in the process of being replaced by a more efficient design), have a Q0 = 32 000; with Rp = 1 MΩ, and operate at Vpeak = 780 kVp) [16,17].

Useful particularly at high RF voltage and beam power levels, yet another advantage can be designed into a waveguide-type cavity: less sensitivity to higher order modes. The ratio between length and height of a cavity should be chosen such that the higher order modes of such a cavity will not coincide with the higher harmonics of the fundamental frequency, so they will not get excited by such harmonic frequency components coming from the final amplifier. This fact also has some consequences for the final amplifier stability. Since the higher harmonics get reflected back into the amplifier, some harmonic component absorption scheme might have to be employed in the transmission line between amplifier and cavity.

With the obtainable high Rp value, very high acceleration voltages (for cyclotrons) are possible; the new replacement cavity for the PSI ring cyclotron, for example, is designed for a peak RF voltage of 1.4 MVp, with a shunt impedance Rp ≈ 1.8 MΩ and a Q0 = 45 000 [17]. Unfortunately, this voltage is not available across the full acceleration gap; it has a sinusoidal distribution (in the fundamental H101 mode). This implies that single gap cavities need some space to extend into the centre region of the machine — past the innermost particle radius — to present some acceleration voltage at inner radii.

Fig. 14: Acceleration voltage distribution in ‘box’ type cavity; acceleration gap along ‘Z’- axis

A general conclusion is therefore that single gap cavities are probably best suited for larger ring cyclotron designs (final stage in multistage accelerator), and that double gap cavities are probably better suited for smaller first stages or lower energy cyclotrons.

There are working (or planned) examples of all cavity designs mentioned; here is a list of a few representative types:

X

Z

Ey

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Table 1: Some representative acceleration cavity types for cyclotrons of the SSC type (Note: RT = room temperature, normal conducting; SC = superconducting; SS = separated sector machine)

Type of resonator Operating frequency Typical Q0-value Name of lab/machine; special features Double gap, λ/4 resonator; RT

variable (2 – 60 MHz) 2000–8000 Numerous ‘classical’ cyclotrons, (with ‘Dees’) → ‘movable short’ or ‘panel’ tuning system

Double gap, λ/2 resonator; RT

6–14 MHz 6500–14000 GANIL/SSC; SS machine, RT magnets → ‘capacitive’ tuning system

Double gap, λ/2 resonator; RT

fixed (51 MHz) 28 000 (Al) PSI/Injector II; SS-machine, RT magnets

Double gap, λ/2 resonator; RT

18–38 MHz 14 000–16 000 RIKEN/RRC; SS machine, RT magnets,

→ ‘box’ tuning system

Single gap resonator: RT

30–52 MHz 18 000–25 000 RCNP/Ring cyclotron;

→ ‘flap’ tuning system

Single gap resonator: RT

fixed (51 MHz) 32 000 (Al) 48 000 (Cu)

PSI/ring cyclotron; very high voltage & load

Single gap resonator: SC

fixed (170 MHz) > 108 (!) TRITRON; fully SC, (incl. magnets)

Under construction: Single gap resonator: RT

18–38 MHz 25 000–34 000 RIKEN/RIBF/SRC; with SC magnets → ‘flap’ tuning system

4.7 Mechanical engineering and design features for cavities

A room-temperature cavity of either double- or single-gap design can be constructed as either an integrated cavity or as a ‘conventional’ cavity, where a separate RF resonator is mounted inside a vacuum chamber — the ‘separate boxes’ design. A superconducting cavity will always be of the ‘separate boxes’ design.

An ‘integrated cavity design’ means that the cavity structure (the resonator) serves a double function as a vacuum chamber with RF properties; the cavity wall generally consists of just one layer. The inner surface of a vacuum tank has to satisfy the conditions for an RF resonator; that is: geometry and surface conductivity are given. On the outside, the dissipated RF power plus the atmospheric load forces have to be taken care of. On the contrary, a conventional cavity, which we call ‘separate boxes’ design (in lack of an generally accepted term for this type of resonator) is built such that a complete RF cavity — including its cooling system, power couplers, tuning elements and probes (pick-ups) — sits inside a vacuum vessel; the cavity walls will therefore always be double-layered, but with clearly separated functions. The inner box — the actual RF cavity — typically is being made of copper, with cooling lines attached to its outer surface, to take up the thermal load of the RF losses, while the outer wall acts as a vacuum chamber only, designed to withstand the atmospheric pressure. This vacuum chamber is typically made of stainless steel, or aluminium.

If one tries to list advantages and disadvantages of the two types of cavity constructions, it becomes clear that such a list applies to single-gap as well as double-gap cavity designs. The only difference may be cooling: in a single-gap cavity, all cooling takes place on outside walls, since there is no inner conductor. This has consequences on long-term reliability: after 25 years of operation, PSI’s injector cyclotron (classical design, one Dee) develops more and more internal cooling leaks, causing long shutdown periods for repair. In contrast, the integrated ring cyclotron cavities (same age) do not show such a decrease in reliability.

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Table 2: Mechanical design of SSC cavities; advantages/disadvantages of integrated or ‘separate cavity in vacuum tank’ designs

Integrated RF cavity Separate RF cavity in vacuum tank Advantages

Vacuum surface (pumping!) is only 1/3rd of separate RF cavity in vacuum tank design

Electrical characteristics (inner shape) and cooling functions can be separated from the vacuum tank design: → heat removal (with thermal effects) can be optimized, independent of the vacuum tank loads

RF power couplers, tuners and pick-ups are simpler; only one wall: → ease of maintenance

Manufacturing of components easier (and cheaper) than integrated design

Most effective use of volume between magnets, available for actual RF cavity

A double-gap cavity can be made of two shells, separated at median plane: → smaller units, cheaper

If designed without electrodes, the cavity is empty: → high Q0, simple el. design

Disadvantages Complex mech. design; RF and mechanical design are combined, because thermal effects and vacuum loads cannot be treated separately

More components (RF cavity and cooling, pick-ups and tuning) are inside vacuum chamber: maintenance more complicated and time-consuming

Manufacturing of cavity more demanding and complex: → more expensive (?)

Typical examples Double-gap design: PSI, ring cyclotron RIKEN RIBF; RRC, acceleration cavities

Single-gap design: PSI, injector cyclotron

RIKEN RIBF; SRC,IRC accel. & flattop cavities TRITRON; superconducting!

Tools: As mentioned earlier — in Sections 4.1 and 4.2 — especially for the case of integrated cavities, the application of sequential coupled field analysis is essential for optimal design procedures [15]. Ultimately, for the next generation of large cyclotron cavities, mechanical constraints, material properties and limits imposed by different manufacturing technologies (and costs!) will play a decisive role in the choice of the final design, which may not be the maximum ‘electrical’ performance but an optimized version with respect to both electromagnetic and mechanical engineering considerations.

5 Frequency tuning systems

5.1 Fixed-frequency cavities

Since fixed-frequency cavities only need fine tuning for the one operating frequency, their design is much simpler, and usually the reliability is better. According to several operators of RF systems with variable frequency range, (like Ref. [18], and private communication), the coarse (wide range) tuning systems have a relatively high failure rate (unscheduled maintenance and repair) due to their technical complexity. Fine tuning devices — usually plungers or capacitive trimmers — have to carry much less current than the movable shorts or flapping panels that are used for large frequency variations. For applications like in ADS systems, which will demand very high reliability and availability at reasonable costs, fixed frequency systems are probably an optimal solution.

In the case of big, box-shaped, integrated cavities like the ones employed in the PSI ring cyclotron (see Fig. 11), the fine tuning can be done by hydraulically squeezing the side-walls of the cavity about the median plane; by a maximum displacement in the beam plane of about 5 mm per side

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(corresponding to less than 2% of the gap width). This generates a Δf/f0 = 1.1%, ( Δf = 550 kHz), more than sufficient to correct atmospheric pressure changes and thermal effects acting on the cavity side-walls (see Fig. 11, top left) [15].

5.2 Variable-frequency cavities

5.2.1 Double-gap, coaxial-type cavities

If a cavity is designed with a λ/2 or λ/4 coaxial structure, large frequency tuning ranges are most often achieved by:

a) movable (sliding) shorting plane at the inductive end of the resonator; or by:

b) using a fixed short, and vary the characteristic impedance Zl of the current end section of a transmission line, thereby changing the effective length; or, alternatively, (obtaining the same effect) by changing the impedance at the capacitive end of the resonator.

c) Finally, one can use movable sections of (lower) characteristic impedance inside the coaxial lines, thus again varying the effective length of the resonator.

Examples of systems of type a) are numerous, and employed for instance in superconducting magnet cyclotrons, like the Milano (Catania, INFN) design, (Ref. [1]), or the NSCL machines.

The type b) design is also widespread, an example is the Texas A&M cyclotron, also shown in Ref. [1]. The impedance variation is obtained by moving panels, which, in effect, change the volume (and Z0) of the end section if a coaxial resonator. GANIL [19] employs a different strategy: the frequency tuning is performed at the capacitive, high-voltage end (the ‘Dee’) of a λ/2 cavity. The first case has to overcome problems of high current loads in panel hinges, while tuning at the ‘Dee-end’ requires careful design to guarantee the voltage holding capacity (sparking).

The type c) design finally is successfully employed in λ/2 cavities in the RIKEN ring cyclotron (RRC), [20]. There, it is called the ‘movable box’ frequency tuning (Fig. 15). This box is galvanically connected only to the outer conductor surface via sliding contacts; the main advantage stems from the fact that the circumference path along the outer conductor is much longer, therefore the current density (in A/cm) for the sliding contacts is much lower than if the contact were made to the inner conductor. Also, cooling of the outer the shell of a resonator is usually easier than of the inner conductor.

Fig. 15: A λ/2 double-gap cavity; f- variation and vertical symmetry tuning with ‘movable boxes’ (RIKEN)

Resonance frequency variation and vertical symmetry is obtained by vertically moving two boxes inside the cavity. Contact fingerstock connects the boxes to the outside wall of the cavity.

λ/2 Key Specifications: Freq. range = 18 - 45 MHz

Max. gap voltage = 300 kVPower dissipation = 150 kW

Q0 = 12'000

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5.2.2 Single-gap, waveguide-type cavities

Such cavities are usually designed for even higher Q0 values and higher acceleration voltages than their coaxial counterparts, and, due to the lack of internal parts (no inner conductor), the technical possibilities for frequency tuning over a wide range are somewhat more limited. Since the resonance frequency of such a ‘box’ is usually defined by two key dimensions — the height a and the length d in Fig. 13 — and the dimension along the acceleration gap should remain constant, varying the height by symmetrically moving top and bottom walls is the obvious way to obtain the frequency variation. This method is employed in the flat-top cavity design of the RCNP ring cyclotron [18]; as well as in the two cyclotrons (IRC and RRC) of the future RIKEN RIBF, also for flat-topping [8].

For even higher voltage levels (as for accelerating cavities), a different approach for resonance frequency variation was chosen: the ‘moveable flap’ design [8],[18]. This concept achieves respectable acceleration voltages (up to 500 kVp @ 38 MHz). Critical components are the hinges, they have to carry the panel currents to the cavity wall. Such cavity tuning systems can no longer be calculated in closed form, or with simple numerical models. Only full use of advanced 3D codes will allow opti-mized designs, together with careful measurements on scale models [8].

Fig. 16: Single-gap, waveguide-type cavity, with ‘movable flap’ frequency tuning system (RCNP)

6 Power coupling into cavities

6.1 Inductive couplers

As mentioned before, inductive coupling is the only practical way to feed RF power into a waveguide- type cavity, since there is no inner conductor to efficiently use capacitive coupling. Basically, the inductive couplers are similar in all RF cavities. An analytical approach to determine the loop area A of an inductive coupler for 50 Ω input impedance, (coupling into a box shaped cavity in the median plane) is usually very unreliable (off by at least a factor of 2, or more), but gives a rough lower limit:

l f0

dA K Z Rω μ

= ⋅ ⋅ ⋅⋅

; (3)

under idealized conditions, (loop wire dia. ≈ 0, homogeneous field distribution, etc.); with d = length of cavity, K a geometry-dependent factor, Zl = 50 Ω, and Rf = surface resistance of cavity material.

Key Specifications: Freq. range = 18 - 40 MHz

Max. gap voltage = 500 kVPower dissipation = 70 kW Q0 < 37'000 (theor. value)

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However, it is relatively easy to get good experimental data: one takes a simple wire loop and varies the shape and size until the desired matching impedance (usually ≥ 50 Ω) is reached, for example by measuring S11 with the help of a network analyser. When high beam loads are expected, the input impedance of a cavity can be set to be as high as 80 Ω, such that optimal impedance match (to 50 Ω) is obtained at high beam load levels. This way, variable coupling loop installations can be avoided, because they are mechanically complex designs and therefore potential sources of RF system failures at very high power levels. Variable size loops are unavoidable in variable frequency cavities, as for example in the RIKEN RIBF resonators [8].

Only recently, with the availability of 3D codes with time domain modules, has it become possible to model the coupling loop region in a cavity more accurately; at the same time, such methods also permit optimized vacuum window designs in RF power couplers [21].

Fig. 17: Inductive RF power coupler for 600 kW (CW) with spark detection electrode (PSI ring cyclotron cavity)

6.2 Capacitive couplers

Capacitive coupling is widely used in double gap, coaxial type resonators, because the inner con-ductor presents an ideal opportunity to couple via a capacitance to the high voltage end (typically the 'Dee structure'); and be independent of geometry changes at the inductive end of the resonator, espec-ially if that end is used for frequency tuning (see Fig. 12). Matching the cavity to a 50 Ω transmission line with a suitable capacity usually presents no special problem; a further advantage can be that a variable capacity (= variable distance of the coupler to the ‘Dee’) is usually easier to design — and will operate more reliably — than a variable area inductive coupling loop (usually obtained by rotation).

A further advantage — compared to an inductive coupler — turns out to be that a capacitive coupler can be biased with a DC voltage, to suppress multipacting in the coupling region and around the ceramic window of such a coupling device.

7 RF power amplifiers

7.1 Characteristics, requirements, concepts

Operation mode: mostly CW, pulsing can be used for start-up (to overcome multipacting in cavities)

Cylindrical ceramic (alumina) window

50 Ω coaxial feeder line

Vacuum side (cavity)

Water cooled coupling loop

Air side

Spark detection electrode

Finger stock contact ring

O- ring

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Operating frequencies: from ≈ 2 MHz to ≈ 200 MHz

– Variable-frequency amplifiers: → extensive remote controlled tuning circuitry required. Frequency range: if possible choose in commercial broadcasting domain (e.g. short wave range, ≈ 6–26 MHz; or low TV or FM broadcasting range. Important simplification: no high-power modulators (like in SW broadcasting) are required.

Advantages: ‘Off-the-shelf’ amplifier chains are available at reasonable conditions (costs, delivery time). Wide power range available (several 100 kW is no problem). Automatic (remote controlled) frequency tuning of amplifier is usually included. High reliability; long term availability of spare parts is guaranteed.

– Fixed operating frequency power amplifiers:

First, also look at commercial amps (TV, FM broadcasting). Alternatively, have amplifiers custom built (very few manufacturers) or acquire ability to design and build them yourself, especially if you require ‘exotic’ frequencies or very high power (knowledge base will be useful for improving and modifying RF systems later).

Amplifying (active) components – Driver stages: solid-state designs, used up to 10 kW.

– Final stages employ power tetrodes used for communication: air- or water-cooled, metal-ceramic constructions.

Life expectancy: >18 000 hrs operation time, if properly protected. Gain: ≈ 13 dB in grounded grid configuration. Robust: → sparking in cavities (Dees) does not damage tube with proper protection measures. High efficiency (60–70%, defined on wide-band 50 Ω load).

Important: When specifying the output power of a final stage amplifier, sufficient power reserve (≈ 30%) should be included, to provide for the regulation range of the amplitude (cavity voltage) control system; and for ageing.

7.2 Types of power amplifiers

7.2.1 Discrete components (L, C) in grounded cathode configuration

Fig. 18: Commercial short wave transmitter, 4–26 MHz, 500 kW RF output power. Simplified block diagram ( left) and picture of the open final amplifier cabinet (right). Shown is the model TSW 2500, by THALES.

Power tube (tetrode)

Power tube (tetrode)

Power Output

RF Output

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7.2.2 Coaxial, concentric amplifier design, grounded grid configuration

Fig. 19: Simplified schematic diagram (top), and cross-sectional view of PSI’s new 150 MHz/220 kW power amplifier (right) [22]. All components in the schematic are built as coaxial lines, which are concentrically arranged around each other. The left part of schematic is the innermost coaxial line, the output coaxial lines are on the outside. The shading in both images matches, that is: represents corresponding components.

8 Cyclotron RF control systems

8.1 Control loop identification

The principal control loops (or control circuits) in any cyclotron RF system are the following:

– Amplitude (= cavity/Dee voltage) control system. It includes the pulsing/ramping circuitry (if required), and also the RF, cyclotron and safety interlock access ports.

Typical stability values that can be obtained are: Vnoisepp/Vcavp < 2 ·10–4 pp.

A word concerning cavity voltage turn-on (pulsing/ramping) procedures: [23].

After limiting amplifiers with dynamic ranges of > 60 dB, with low phase shift, became available, it was possible to tune resonators at very low power levels (below multipacting levels), then ‘punch’ rapidly through the multipacting regions (with short pulses), and to continue to ramp to the required cavity operating voltage as soon as the pulse on the cavity rose above the multipacting level. Such a control signal is shown below on the left (Fig. 20).

– Frequency tuning system (it might be split into coarse and fine tuning)

Different actuators can be used; the most popular types are

Stepping motors (with or without gears), suitable if control element (e.g. trimmer) is not continuously moving (e.g. coarse tuning).

Hydraulic actuators are used when fast, continuous corrections are required, or in case of heavy mechanical load (large mass, or vacuum forces).

Power tube (tetrode)

AC

G1 G2

λ/4 λ/4

λ/4 λ/4 λ/4

λ/4

λ/4

λ/2

n·λ/2

λ/4

RF INPIN = 10 kW50 Ω

Power tube (tetrode)

AC

G1 G2

λ/4 λ/4

λ/4 λ/4 λ/4

λ/4

λ/4

λ/2

n·λ/2

λ/4

RF INPIN = 10 kW50 Ω

RF OUTPOUT = 220 kW

50 Ω

Power tube

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– Phase control system — required only if a cyclotron consists of more than one independent amplifier/Dee system and/or is used in a multistage configuration (more than one accelerator connected in series). Phase noise (peak–peak) can be held to < 0.05º pp.

Fig. 20: Turn-on signal (left), and RF signals in a 200 μs pulse: off resonance, and on resonance. Duty cycle: ≈ 1%.

Fig. 21: Block diagram of a typical (generic) RF control system, showing the three principal control loops

8.2 Control loop optimization, ground loops

When control loops are designed, gain and bandwidth optimization is usually carried out according to the rules for small signal (linear) control theory. This is legitimate — contrary to transmitter design, we usually do not want any modulation at all. Often though, the theoretically possible suppression of the distortion, hum and noise cannot be reached. Mostly, this is due to ground loops — the concept is usually considered only when most of the hardware is already in place. Below is an illustration of the effect: shown are the frequency spectra of the demodulated cavity voltage signal. The same concept applies to all other high bandwidth control loops, of course.

Preflect

Interlocks

Vcav

Pos. Ref.

Servo-Unit

Cavity

Pincident

+

Limitingamps

VCav.Pickup

StartupUnit

ControlUnit

Volt. Ref.

Pos.

Se

nsor

M.O.

Mixer

Ampl.-Controller

Pin

20W Ampl. 800kW Final Ampl.

Delay

φ- Controller

φCavPickup

f-tuningActuator

RF- Reference

Preflect

Interlocks

Vcav

Pos. Ref.

Servo-Unit

Cavity

Pincident

+

Limitingamps

VCav.Pickup

StartupUnit

ControlUnit

Volt. Ref.

Pos.

Se

nsor

M.O.

Mixer

Ampl.-Controller

Pin

20W Ampl. 800kW Final Ampl.

Delay

φ- Controller

φCavPickup

f-tuningActuator

RF- Reference

Prefl turn-off RF on

Minimum level

Pulse

Red.power

Switching point: Pinc → Ucav

Delay RampPrefl turn-off RF on

Minimum level

Pulse

Red.power

Switching point: Pinc → Ucav

Delay Ramp

Turn-on procedure of cyclotron cavity voltage, with pulsing and ramping

RF Pulse with cavity on resonance

Incident power

Reflected power

Cavity voltage

Incident power

Reflected power

Cavity voltage

RF Pulse with cavity detuned, or multipacting

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Fig. 22: Amplitude control loop frequency spectra: open loop and closed loop; effect of a ground loop

Acknowledgements and conclusion The author wishes to thank all those colleagues who generously supplied information material for inclusion and reproduction in this paper.

Special thanks go to C. Pagani and U. Trinks, the colleagues at GANIL, as well as A. Goto and his group (RIKEN), for letting me use their excellent material. Of course, I would also like to thank my own colleagues from the PSI RF team, especially H.R. Fitze, M. Bopp and L. Stingelin for their material on cavity design, W.Tron and M. Schneider for pictures on power amplifiers, and J. Cherix for data on control systems.

Cyclotron RF design is still a very exciting field, open for new ideas and concepts, especially in view of the new design tools that have recently become available. New fields for cyclotron applications have opened up — like ADS with HPPAs, compact SC medical cyclotrons, or even fully superconducting cyclotrons (including SC RF cavities).

In the applications mentioned, the prevention of frequent sparking in cavities (causing beam trips) is becoming increasingly important. This will call for more and intensified studies of discharge and voltage breakdown mechanisms and multipacting phenomena in cavities. It is hoped that ultimately these investigations will lead to a reduction in the number of beam interruptions in cyclotrons caused by RF systems. At the same time, machines will have to be designed with higher efficiency in mind (also a new aspect in cyclotron design), and further improved reliability and reduced operational costs: cyclotrons of the future will be measured by the same criteria applied to other ‘high-tech’ industrial products.

References [1] C. Pagani, Cyclotron Cavities, CAS Proceedings, CERN 92-02 (1992), pp. 501–521.

[2] NEA/OECD Proc. of Workshop on Utilisation and Reliability of High Power Accelerators, Mito, Japan, 1998.

[3] C. Rubbia et al., Proc. EPAC, (1994), pp. 270. N. Fietier et al., CERN Report AT-95-03(ET), (1995).

[4] PSI Scientific Report, Vol. VI (1999), p. 4.

[5] M. Eriksson et al., NEA/OECD Proc. of Workshop on Utilisation and Reliability of HPPA, Mito, Japan, 1998, p. 183.

Open loop frequency spectrum

Closed loop frequency spectrum

Closed loop frequency spectrum.

With ground loop

Closed loop frequency spectrum. Without

ground loop

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[6] P. Sigg et al., NEA/OECD Proc. of Workshop on Utilisation and Reliability of HPPA, Mito, Japan, 1998, p. 199.

[7] NEA/OECD Proc. of Workshop on Utilisation and Reliability of HPPA, Aix-en-Provence, (Nov. 1999), p 175.

[8] N. Sakamoto et al., Proc. of the 15th Intl. Conf. On Cyclotrons & Appl., (1998) p. 223. N. Sakamoto et al., Proc. 12th Symp. on Accel. Sci. and Technology, Wako (1999) p. 224.

[9] U. Trinks et al., Proc. of the 12th Intl. Conf. On Cyclotrons & Appl., (1989) p. 47. U. Trinks et al., Proc. of the 15th Intl. Conf. On Cyclotrons & Appl., (1998), p. 323, p. 693.

[10] P. Sigg, Proc. of the 12th Intl. Conf. On Cyclotrons & Appl., (1989) p. 212.

[11] P. Sigg et al., Proc. of the 13th Intl. Conf. On Cyclotrons & Appl., (1992) p. 534.

[12] J. N. Corlett, Experience with cavity design programs CAS, CERN 92-02 (1992), pp. 301–315.

[13] L. Stingelin, Ph. D. thesis # 3169, EPFL, Lausanne, (Jan. 2005).

[14] M. Bopp, H. Fitze, PSI Scientific and Technical Report Vol. IV (2001), p. 9.

[15] M. Bopp, H. Fitze, 22nd CAD-FEM Users Meeting, Dresden (D), Nov. 2004.

[16] H. Fitze et al., Proc. of the 1999 PAC, Vol. 2, p. 795.

[17] H. Fitze, M. Bopp, PSI Scientific and Technical Report Vol. IV (2002), p. 50; (2003), p. 44.

[18] T. Saito et al., Proc. of the 12th Intl. Conf. On Cyclotrons & Appl., (1989) p. 201.

[19] C. Bieth et al., IEEE Trans. on Nucl. Sci., NS-26, (1979), p. 4117.

[20] T. Fujisawa et al., Proc. of the 10th Intl. Conf. On Cyclotrons & Appl., (1982) p. 311. T. Fujisawa et al., Proc. of the 11th Intl. Conf. On Cyclotrons & Appl., (1986) p. 329.

[21] P. Sigg et al., Proc. of the 14th Intl. Conf. On Cyclotrons & Appl., (1995) p. 165.

[22] M. Maerki, W. Tron, M. Schneider; private communication (to be published).

[23] J. Cherix, P. Sigg, PSI Scientific & Technical Report Vol. IV, (2004), p. 16.

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