Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP44

CONCEPTUAL DESIGN OF A HIGH TEMPERATURE
SUPERCONDUCTING SPECTROSCOPY-TYPE GANTRY SYSTEM FOR
PARTICLE THERAPY
H. Zhao∗ , M. Fukuda,T. Yorita, H. Kanda, Y. Yasuda, D. Tomono, K. Hatanaka,T. Saitou,S. Morinobu, Y. Morita, K. Takeda, T. Hara, T. Chong, M. Kittaka, S. Matsui,
K. Watabe, T. Imura, Research Center for Nuclear Physics (RCNP), Osaka, Japan
Abstract
Radiation therapy is a kind of extremely efficient cancer
treatment that uses high doses of radiation to kill cancer cells.
In radiation therapy with high energy particles, the dose isusually applied to the tumor with irradiation from several
directions, to limit the dose in healthy tissue in vicinity ofthe tumor. In order to realize a continuous angular range ofirradiation, a spectroscopy-type beam delivery device (i.e.
the gantry) is proposed. In the conception of spectroscopytype gantry, beam is guided to the appropriate azimuthal
angle with cylindrical magnetic field surrounding the patient, and treatment angles are set by adjusting magnetic
strength, instead of rotating a gantry with magnets of thebeam transport around the patient. With this conception as
well as high temperature superconducting materials, continuous angular range of irradiation could be realized bya super compact spectroscopy-type gantry. In this work, aconceptual design of a high temperature superconducting
spectroscopy-type gantry system with a scanning system will
be present.

therapy gives a lower burden to patient body, and fewer sideeffects.

Gantry System
In order to acquire multiple treatment angle so that a better
dose distribution in the target and better protection of healthy
tissue around the target, a design of rotating gantry system
is proposed. The rotating gantry system rotates around thepatient to get several treatment angle (see Fig. 2), so thatthe dose in healthy tissue in vicinity of the tumor can beoptimized. However, in a rotating gantry system, magnets

INTRODUCTION
Particle Therapy

Figure 2: Schematic view of a rotating gantry system, magnets are mounted in gantry rings and rotated with rollerassemblies to acquire planned treatment angles. Illustration
provided by Johns Hopkins Proton Therapy Center.

Figure 1: Therapies against cancer.
Radiation therapy (also called therapeutic radiation treatment) is a cancer treatment that uses high doses of radiation
to kill cancer cells or slow their growth by damaging their
DNA. Cancer cells whose DNA is damaged beyond repair
stop dividing or die. When the damaged cells die, the arebroken down and removed by the body. Radiation therapy
does not kill cancer cells right away. It takes days or weeks
of treatment before DNA is damaged enough for cancer cells
to die. Then, cancer cells keep dying for weeks or months
after radiation therapy ends. Compared to conventional surgical therapy and chemical therapy listed in Fig. 1, radiation∗ zhao@rcnp.osaka-u.ac.jp

are mounted in the gantry structure and rotated with large
mechanic arm, making it too huge for many facilities to introduce. The large dimensions (8-12m diameter) and masses(100-200 tons) of the proton gantries [1] limit the rotational
speed to 1 turn/min for safety measures preventing possible
collisions [2]. Besides, the mechanical system in rotating
gantry system also restricts the available treatment angles toseveral preinstalled ones, which may limit treatment planning in some cases.

PURPOSETo realize the compactness of gantry system, as well as
continuous treatment angles for a better dose distribution, weare designing a HTS (High Temperature Superconducting)Spectroscopy-type Gantry System with pencil beam scanning irradiation. In the HTS Spectroscopy-type Gantry System, no heavy magnets require to be rotated while applying
treatment in an arc, allowing a simpler mechanical structure- 410 -

Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP44and rapid treatment. The purpose of the HTS Spectroscopytype Gantry System is illustrated in Fig. 3.

Figure 4: Schematic of cross section of a dipole magnet [3].
Eq. (1) along a closed path like the one shown in Fig. 4 andusing Stokes’ theorem gives
𝐵

2𝐺𝐵0 + ∫𝑖𝑟𝑜𝑛 𝜇𝑟

Figure 3: Purpose of a Spectroscopy-type Gantry. Beam are
injected from a certain point and transported to a desired
treatment angle.
The HTS Spectroscopy-type Gantry System is designed
to provide continuous treatment angles in a range of 180∘ ,from the vertical upside (0∘ Irradiate) to the vertical downside(180∘ Irradiate). With a rotating treatment table set to 0∘ or180∘ , continuous treatment angles in a range of 360∘ areactually realizable.
The internal magnetic field strength is estimated to beover 2T, which is hard for common conductor to generate.
Therefore, superconducting coils is considered to be necessary for the design. For a better secure operation reliability,
which is the most essential point for a medical device, aswell as a higher current density in superconducting coil, we
decide to use HTS material for the coils.
With spectroscopy-type design and HTS material, thisdesign of gantry system is expected to be super compact
comparing to the traditional gantry system.

THEORY
Design Characteristics of Dipole Magnets
A dipole field can be generated, for example, in an electromagnet as shown in Fig. 4 where the beam would travel
normal to the cross section into the center of the magnet.Themagnetic field 𝐵 is generated by an electrical current I in current carrying coils surrounding magnet poles. A ferromagnetic return yoke surrounds the excitation coils providing
an efficient return path for the magnetic flux. The magnetic
field is determined by Ampere’s law∇×𝐵= 𝜇0 𝑗𝜇𝑟(2)where 𝐵0 is the magnetic field in the center of the magnet
aperture between and normal to the parallel magnet poles
with a gap distance of 2𝐺. The integral term in Eq. (2) is zeroor negligibly small in most cases assuming infinite or a verylarge permeability within the magnetic iron. 𝐼𝑡𝑜𝑡 = 2𝐼𝑐𝑜𝑖𝑙
is the total current flowing in the complete cross section ofboth coils. Solving Eq. (2) for the total current in each coil
we get in more practical units
𝐼𝑐𝑜𝑖𝑙 (A) =10

B0 (T)G(m)(3)

which is proportional to the magnetic field and the aperture
between the magnet poles.

Particle Beam Guidance
Assuming in general that the magnetic field vector 𝐵 is oriented normal to the velocity vector 𝑣, linear beam dynamics
can be restricted to purely transverse fields. The restriction
to purely transverse field components has no fundamental
reason other than to simplify the formulation of particle
beam dynamics. While use a curvilinear coordinate system(𝑥, 𝑦, 𝑧) following the ideal path, it is necessary to follow aparticular particle trajectory for the coordinate 𝑠. Then thebending radius for the particle trajectory in a magnetic fieldis𝑒𝑐
𝜅𝑥,𝑦 = ∓𝐵(4)𝛽𝐸 𝑦,𝑥For multiply charged particles like ions, the electricalcharge 𝑒 in all equations must be replaced by 𝑒𝑍 if, for example, ions of net charge 𝑍 are to be considered. Since it
is also customary not to quote the total ion energy, but theenergy per nucleon, Equation (4) becomes for ions
1𝑍 |𝐵|= 0.2998
𝜌𝐴 𝛽𝐸

(1)

where 𝜇𝑟 is the relative permeability of the ferromagnetic
material and 𝑗 is the current density in the coils. Integrating𝑑𝜎 = 𝜇0 𝐼𝑡𝑜𝑡(5)where 𝐸(GeV/u) is the total energy per nucleon and A theatomic mass.

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Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP44

Figure 5: a. Front view of designed structure of the HTS Spectroscopy-type Gantry System. Magnets poles for guiding
area and bending area are illustrated in light gray and dark gray. Treatment area is within the range of inner coils. b. Side
view of the structure. Pole gap in bending area and guiding area is designed respectively.

Dispersion Function
The general solution of the equations of motion withhigher order parameters then is given by the combinationof the two principal solutions of the homogenous part ofthe differential equation and a particular solution for theinhomogeneous differential equation𝑢(𝑧) = 𝑎𝐶𝑢 (𝑧) + 𝑏𝑆𝑢 (𝑧) + 𝛿𝑃𝑢 (𝑧)(6)where the coefficients 𝑎 and 𝑏 are arbitrary constants to bedetermined by the initial parameters of the trajectory. Index
𝑢 is used to indicate that these functions must be defined separately for 𝑢 = 𝑥 and 𝑦. A general solution for the equationof motion for any perturbation is derived in Eq. (6), and set
𝑃𝑢 (𝑧) = 𝛿𝐷𝑢 (𝑧),𝑧𝐷𝑢 (𝑧) = ∫ 𝜅0𝑢 (𝑧)[𝑆̃ 𝑢 (𝑧)𝐶𝑢 (𝑧)̃ − 𝐶𝑢 (𝑧)𝑆𝑢 (𝑧)]𝑑̃ 𝑧̃
0(7)Beam Sizes
The beam parameters for a Gaussian particle distributions
are defined as the standard values of the Gaussian distribution �𝜎𝑥 , 𝜎𝑥′ , 𝜎𝑦 , 𝜎𝑦′ , 𝜎𝛿 , 𝜎𝑙 , where most designations
have been defined and used in previous chapters and where�𝜎𝛿 = 𝜎𝜖 /𝑐𝑝0 and 𝜎𝑙 the bunch length. Quoting beam sizes
for any particle type in units of 𝜎 can be misleading specifically in connection with beam intensities. For example, abeam with a horizontal and vertical size of one sigma has
a cross section of 2𝜎𝑥 2𝜎𝑦 and includes only 46.59% of thebeam. This is accepted for electron beams with Gaussian
distribution but for proton beams intensities are often given
for √6𝜎’s to cover most of the beam. The fraction of thetotal beam intensity is compiled for a few generally usedunits of beam size measurement and for beam size, crosssection, and volume. The beam size for Gaussian beams isthereby
𝜎𝑢,𝑡𝑜𝑡 (𝑧) = √𝜖𝑢 𝛽𝑢 (𝑧) + 𝜂2 (𝑧)𝜎2𝛿
(8)

CONCEPTUAL DESIGN OF THE HTSSPECTROSCOPY-TYPE GANTRY SYSTEM
Structure Configuration
The structure configuration of the HTS Spectroscopy-type
Gantry System is illustrated in Fig. 5. Treatment table islocated at the center of the gantry system. Beam is transported from the left side and injected in the gantry systemwith an Injection Scanning Magnet (ISM), then guided tothe target by the internal magnetic field. Internal magnetic
field is separated to 3 areas, guiding area, bending area andtreatment area. After injection, beam will be guided to acertain angle in guiding area then bended toward to target inbending area and irradiate the target in treatment area.
Magnetic fields in all area is excited by the outer coils, andthe inner coils cancel the magnetic field in the treatment area.
Magnetic field in guiding area and bending area is different
and adjusted by the pole gap in each area. ISM is used to set
treatment angle by bending the beam appropriately during
the injection.

Internal Magnetic Field Profile Simulation
The internal magnetic field profile is simulated byOpera3D Simulation Software. For a simpler calculationof particle trajectory, we investigated the magnetic fieldstrength along the radius (𝑟𝐺 ) direction, instead of 𝑥, 𝑦 axis.
Figure 6 shows the extracted magnetic field profile as a function of radius in the midplane. Then we can calculate thetrajectory of single particle.

Particle Trajectory Calculation
With the result of magnetic field profile simulation, now
we can calculate the particle trajectory in the gantry system. We start the particle trajectory at the treatment tablereversely, and calculated the trajectory through the gantrysystem to the ISM. With the simulation result in Fig. 6, we- 412 -Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP44

Figure 6: Magnetic field profile in the midplane simulatedby OPREA. The peak of 𝐵𝑧 in bending area is about 2.46 T.
In guiding area, 𝐵𝑧 keeps at about 0.79 T.
can solve the equation of motion for a particle at a certain 𝑟𝐺 .
Therefore, this time we need to use numerical calculation
to calculate the particle position change and slope of thetrajectory change within a time step change (Δ𝑡 = 10−10 s).
For the approximate calculation, we only considered the 1storder parameter in the equation of motion.
Figure 7 shows the calculated particle trajectory in themidplane of the HTS Spectroscopy-type Gantry System,
for treatment angle 𝜃 from 0∘ (vertical irradiation) to 180∘(vertical irradiation from the back), using 230MeV protons.
Beam is transported to the HTS Spectroscopy-type Gantry
System from the left side, and enters the ISM (Injection
Scanning Magnet). Magnetic field in the ISM is controlled
to direct beam onto the designed trajectory designed for acertain treatment angle 𝜃.

𝑟0 and the angle between the tangent line of the trajectory
and the normal of the ISM 𝜑0 at the exit of the ISM. Bothof the injection data are illustrated in Fig. 7.
When we sum up the injection data (𝑟0 , 𝜑0 ) for the treatment angle 𝜃 from 0∘ to 180∘ , we can get a graph in Fig. 8.
The bubble points in Fig. 8 present the injection data foreach treatment angle with a changing step of 10∘ , and thetreatment angles between steps are also valid, which cangive the injection data for continuous treatment angle in therange of 0∘ ∼ 180∘ .

Figure 8: Injection data (𝑟0 , 𝜑0 ) for the treatment angle 𝜃with a changing step of 10∘ from 0∘ to 180∘ (color bar). The
horizontal axis present the injection data 𝑟0 , and the verticalaxis is 𝜑0 .
For example in the case of performing horizontal irradiation (𝜃 = 90∘ ), we need to check the injection data (𝑟0 , 𝜑0 )for treatment angle 𝜃 = 90∘ and control the ISM properly tosatisfy the required injection data, to direct beam onto thedesigned trajectory for horizontal irradiation in Fig. 7.

Beam Spot Size Evaluation

Figure 7: Designed particle trajectory in the midplane of
the HTS Spectroscopy-type Gantry System for 0∘ ∼ 180∘treatment angle (color bar), using 230MeV protons withnumerical calculation.

The beam phase space changes through a trajectory, thus
we need to calculate the phase space changing for each separate trajectory in Fig. 7. Here we will discuss three particle
trajectory designed for representative treatment angle 0∘ ,90∘ and 180∘ .
Table 1: Assumed Initial Parameters for Beam Dynamics
Calculation

In order to control the ISM correctly, beam status, such astransportation axis and direction, at the entrance as well as
the exit of the magnets are required. The beam status at theentrance mainly depends on the accelerator and beam lineadjustment. Therefore, at this phase, we needs to sum up thebeam status required at the exit of ISM, to make sure thatthe beam is transported along the designed trajectory for acertain treatment angle 𝜃. There are 2 necessary injection
data for a designed trajectory, which are the distance from thecenter point of the HTS Spectroscopy-type Gantry System- 413 -Initial Parameters
ParametersValue
𝜖0 10−6 𝜋⋅m⋅rad
𝛽0
1.0 m
𝛼00
𝛾01.0 rad(Δ𝑝/𝑝0 )00.1%
𝐷00m

Proceedings of the 20th Annual Meeting of Particle Accelerator Society of Japan
August 29 - September 1, 2023, Funabashi

PASJ2023 TUP44

Table 2: Calculated Beam Parameters in Bending Plane, Using 230MeV Protons with Constant Emittance 𝜖 = 10−6 𝜋⋅m⋅rad,and Momentum Deviation (Δ𝑝/𝑝0 )0 = 0.1%

𝜃[∘ ]
090
180

Beam Spot Evaluation in Bending PlaneOn Target
On Target
On Target
On Target
Phase
Dispersion Beam Spot Size
Derivative′(𝛽𝑦 , 𝛼𝑦 , 𝛾𝑦 )𝐷𝑦 [m]𝜎𝑦 [𝑚𝑚]𝑦𝑚𝑎𝑥[mrad](1.7, −1.1, 1.3)
2.3
2.6
1.1
(13.4, −9.9, 7.4)
−1.23.9
2.7(2.6, −2.7, 3.1)
−4.8
5.1
1.8

For the calculation, we used 230MeV protons and assumed a beam emittance of 1𝜋⋅m⋅mrad, with constant momentum deviation of 0.1% . Twiss parameters are initially
set as 𝛽0 = 1.0mm, 𝛾0 = 1.0rad and, 𝛼0 = 0 . The parameters for calculation is summed in Table 1.

Beam SpotMax Size𝜎𝑦 [𝑚𝑚]
2.6
4.3
6.0

an actual application, a smaller beam spot size usually gives
a better dose distribution with pencil beam scanning technology. Therefore, a beam spot size as small as possible
is desired in this design. The result with assumed initial
beam condition gives us a beam spot with 1𝜎 = 5.1 mm in180∘ treatment. A beam spot with this size may be a little
hard to create treatment plan with pencil beam scanning,
but completely feasible for an actual treatment comparing
with practically applied beam spot size, e.g., beam spot sizefor pencil beam scanning currently applied in HIMAK (Osaka,JP) is 1𝜎 = 2 ∼ 10 mm.

SUMMARY

Figure 9: Beam phase parameter 𝛽𝑦 and dispersion function
𝐷𝑦 in bending plane during transportation for 180∘ treatment.

Beam Spot Size for 180∘ Treatment
In order to describe the beam spot size along the particle
trajectory in the bending plane caused by both betatron oscillation and momentum dispersion, we need bring 𝛽𝑦 and 𝐷𝑦
into Eq. (8). Therefore, we graphed the 𝛽𝑦 and 𝐷𝑦 along thebeam trajectory in Fig. 9. The beam phase on target is calculated to be (𝛽𝑦 , 𝛼𝑦 , 𝛾𝑦 ) = (2.6, −2.7, 3.1), and a dispersion
function of 𝐷𝑦 = −4.8m.
Then we can observe the beam spot size change duringtransportation. Initial beam spot size can be calculated withassumed beam emittance and 𝛽𝑦0 and 𝐷𝑦 ,which is 𝜎𝑦0 =1.0 mm, and increased to 𝜎𝑦 = 5.1 mm on target. The max
beam spot 𝜎𝑦𝑚𝑎𝑥 = 6.0 mm size is observed at 𝑧 = 10.5 m.

Apply 0 , 90 180 Treatment∘∘∘

With the same calculation, we can observe the on target
beam spot size for each treatment angle, as illustrated inTable 2. By calculating the beam dynamics in transportation for three typical treatment angle, we know that beam
may be defocused in the designed spectroscopy-type gantry
system , and a longer particle trajectory gives a stronger
beam dispersion, for example 180∘ treatment. However, inIn order to realize the compactness and a continuous treatment angle in a range of 180∘ , we are designing a HTS(HighTemperature Superconducting) Spectroscopy-type Gantry
System. In the HTS Spectroscopy-type Gantry System, treatment angle can be set by controlling magnetic field, insteadof rotating the beam line around the patient with huge mechanical arms.
In this step of design, we have designed the basic structure configuration and simulated the internal magnetic fieldprofile. With the simulated magnetic field profile, we calculated the particle trajectory and its injection data for acertain treatment angle in a range of 180∘ , using 1st order inequation of motion. Considering an actual beam transportation system, phase space in beam spot size is also evaluated.
With assumed beam emittance and momentum deviation,
we calculated the beam spot size changing during the transportation for typical treatment angles. The result indicatesthat a certain initial phase of beam may defocus on the target,
max to 1𝜎 = 5.1 mm in 180∘ treatment, but still feasible forthe actual treatment.

REFERENCES[1] Schulze M. E., 1991, Commissioning results of the LLUMG
beam switchyard and gantry, Proc.14th Particle Accelerator
Conf., PAC’91, 610-3.
[2] Nicolini G., Clivio A., Cozzi L., Fogliata A. and Vanetti E.,
2011, On the impact of dose rate variation upon RapidArc
implementation of volumetric modulated arc therapy, Med.
Phys., 38, 264-71.
[3] Helmut Wiedemann et al., (2015) Particle Accelerator Physics(Fourth Edition).

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