Formation of a uniform ion beam using octupole magnets for BioLEIR facility at CERN

The possibility to transform the Low Energy Ion Ring (LEIR) accelerator at CERN into a multidisciplinary, biomedical research facility (BioLEIR) was investigated based on a request from the biomedical community. BioLEIR aims to provide a unique facility with a range of fully stripped ion beams (e.g. He, Li, Be, B, C, N, O) and energies suitable for multidisciplinary biomedical, clinically-oriented research. Two horizontal and one vertical beam transport lines have been designed for transporting the extracted beam from LEIR to three experimental end-stations. The vertical beamline was designed for a maximum energy of 75 MeV/u, while the two horizontal beamlines shall deliver up to a maximum energy of 440 MeV/u. A pencil beam of 4.3 mm FWHM (Full Width Half Maximum) as well as a homogeneous broad beam of 40 × 40 mm2, with a beam homogeneity better than ±4%, are available at the first horizontal (H1) irradiation point, while only a pencil beam is available at the second horizontal (H2) and vertical (V) irradiation points. The H1 irradiation point shall be used to conduct systematic studies of the radiation effect from different ion species on cell-lines. The H1 beamline was designed to utilize two octupole magnets which transform the Gaussian beam distribution at the target location into an approximately uniformly distributed rectangular beam. In this paper, we report on the multi-particle tracking calculations performed using MAD-X software suite for the H1 beam optics to arrive at a homogeneous broad beam on target using nonlinear focusing techniques, and on those to create a Gaussian pencil beam on target by adjusting quadrupoles strengths and positions.

: The possibility to transform the Low Energy Ion Ring (LEIR) accelerator at CERN into a multidisciplinary, biomedical research facility (BioLEIR) was investigated based on a request from the biomedical community. BioLEIR aims to provide a unique facility with a range of fully stripped ion beams (e.g. He, Li, Be, B, C, N, O) and energies suitable for multidisciplinary biomedical, clinically-oriented research. Two horizontal and one vertical beam transport lines have been designed for transporting the extracted beam from LEIR to three experimental end-stations. The vertical beamline was designed for a maximum energy of 75 MeV/u, while the two horizontal beamlines shall deliver up to a maximum energy of 440 MeV/u. A pencil beam of 4.3 mm FWHM (Full Width Half Maximum) as well as a homogeneous broad beam of 40 × 40 mm 2 , with a beam homogeneity better than ±4%, are available at the first horizontal (H1) irradiation point, while only a pencil beam is available at the second horizontal (H2) and vertical (V) irradiation points. The H1 irradiation point shall be used to conduct systematic studies of the radiation effect from different ion species on cell-lines. The H1 beamline was designed to utilize two octupole magnets which transform the Gaussian beam distribution at the target location into an approximately uniformly distributed rectangular beam. In this paper, we report on the multi-particle tracking calculations performed using MAD-X software suite for the H1 beam optics to arrive at a homogeneous broad beam on target using nonlinear focusing techniques, and on those to create a Gaussian pencil beam on target by adjusting quadrupoles strengths and positions.

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: Accelerator Applications; Accelerator modelling and simulations (multi-particle dynamics; single-particle dynamics); Beam dynamics; Beam Optics 1Corresponding author. c 2018 CERN. Published by IOP Publishing Ltd on behalf of Sissa Medialab. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

BioLEIR facility
Advanced radiotherapy using proton, Carbon ion or other ion beams (hadrontherapy) to deliver a maximally effective dose of radiation to a designated tumour site, has gained huge momentum over the last two decades. Many new centres have been built, and many more are under construction. Compared with photon beam radiotherapy, hadrontherapy allows more selective deposition of radiation dose in various cancers while reducing dose to surrounding healthy tissues. Heavier ions (e.g. Carbon ions), in addition, due to the higher density of ionisation events along the particle track, exhibit a higher relative biological effectiveness than X-rays or protons, making them prime candidates for the treatment of also radio-resistant tumours. Still, these advantages are felt to be preliminary, based on scattered physical and biological studies, spread over many years, and performed in heterogeneous centres under different conditions, resulting in significant systematic uncertainties. There is also criticism on the lack of large-scale clinical or preclinical studies data to support assumptions on the effectiveness of hadron therapy [1].
Particle irradiation and the impact in vitro have been reported in a number of publications, resulting in a large range of Relative Biological Effectiveness (RBE) data from a number of different cell lines and endpoints. These studies have been very useful in confirming to a large extent the hypotheses of the effect of particle irradiation. Nevertheless, the heterogeneity between the different studies makes it hard to combine the obtained data and to draw definitive conclusions [1]. A dedicated centre for biomedical research, which is urgently needed, will not only provide the necessary beam time in large time blocks, but also will foster closer collaborations between research teams from different countries to rapidly move the field of hadron therapy forward. Such a dedicated centre will serve to optimise hadron therapy and help current and future hadron therapy centres worldwide, which shall contribute to further improving radiotherapy outcomes and potentially decreasing of mortality rates in cancer patients [1,2]. The Low Energy Ion Ring (LEIR) accelerator at CERN shall provide a beam for a range of light ions from protons up to at least Oxygen for -1 -the purposes of biomedical research [1]. The idea of modifying the existing LEIR accelerator to establish a biomedical research facility (BioLEIR) was suggested during a brainstorming meeting at CERN in 2012 [3]. The optics functions and properties of LEIR accelerator (i.e. duty cycle, ring lattice, families of correctors, and momentum acceptance, etc.) can be found in [1,4,5]. The proposed biomedical research facility at CERN (BioLEIR) has one horizontal (H1) and one vertical (V) irradiation points for biomedical research and a second horizontal (H2) irradiation point for research more related to (micro-)dosimetry development and fragmentation studies. The vertical beamline allows irradiation of cells in the growth medium where the cells can be kept in aqueous phase medium [1,6]. The present LEIR uses only fast beam extraction to the next accelerator of the ion chain eventually leading to the Large Hadron Collider (LHC). To provide beam for a biomedical research facility, a new slow extraction needs to be installed [1]. A short transfer line brings the ions to two horizontal beamlines with energies up to 440 MeV/u (beam rigidity Bρ = 6.7 T.m) for most light ions of interest. A vertical beamline with energies up to 75 MeV/u (Bρ = 2.6 T.m) completes the facility. All energies are kinetic, and quoted for fully stripped Carbon ions 12 C 6+ [6].  The beam transport and matching are constrained by the space available in the South Hall (see figure 1), the optics functions and beam sizes at the LEIR extraction point in both planes (horizontal and vertical), the optics functions at the target positions in both planes, and by the required beam sizes and uniformity at the target planes. The initial conditions at the LEIR extraction point and at the target planes at the beamline extremities are given in table 1. Seven dipoles, twenty quadrupoles, and two octupoles are needed to provide the specified beams for the three beamlines. The main dipole, quadrupole, and octupole parameters are given in table 2. Table 1. Initial and final conditions for the three beamlines matching at the BioLEIR facility. The Twiss parameter α and the dispersion (D) and its derivative (D') are matched to zero at the target in both planes [6].

Extraction beamline octupoles Unit Value
Max beam rigidity T.m 6.7 Magnetic length m 0.33 Nominal strength T.m −3 3 × 10 4 Inscribed pole tip radius mm 50 Nominal pole tip field T 3.75 Number installed (spare) 2 (1) All main dipoles are envisaged to be powered individually to allow for more variables for trajectory correction. It is assumed that there are 5 horizontal dipole converters (i.e. power converters) and 2 vertical dipole converters for the three beamlines.  oct1  oct2  kfh3234  cbed1  cbed2  cbed3  h1bed1  htargetm  scat  qc1  qc2  qcb1  qcb2  qcb3  qc3  qc4  qh1  qh2  qh3  qh4  qh5   0  planes with a FWHM of 4.3 mm (i.e. pencil beam). The whole target area can be irradiated using a scanning system. The beam profiles corresponding to the target front plane, a 10 cm depth in the target, and a 20 cm depth in the target are shown in figure 5. It is noted that the FWHM value of the Gaussian profiles in both planes increases slightly with target depth.

Uniform beam
A uniform broad beam can be obtained by strong beam defocusing and then collimating the defocused beam before the target, allowing only for the central portion (∼2%) of the Gaussian beam to impinge on the target. This mechanism results in high beam loss and activation of the surrounding materials. An alternative is the use of a tail folding mechanism to achieve a uniform transverse distribution, which requires the addition of octupole magnets.The tail folding mechanism has the advantage of increasing the intensity on target, hence reducing irradiation times and lower activation along beamline [7]. This method of generating uniform beam distributions at the target plane is based on magnetically focusing the transported beam by applying nonlinear forces. A beam distribution that is Gaussian in all transverse coordinates can be transformed into an approximately uniform profile in real coordinate space using octupole magnets, where the phase-space ellipse is distorted into an S-shape by the nonlinear force [8,9].
The first horizontal beamline (H1) at the BioLEIR facility was designed to use two magnetic octupole elements (one for each plane) which transform the Gaussian beam distribution at the location of the target into a beam with rectangular cross section, and the beam is approximately uniformly distributed over the irradiated target. Figure 6 shows the two-dimensional distribution of the 440 MeV/u fully stripped Carbon ions beam at the target position at the end of the H1 beamline (broad beam). The beam is focused using two octupole magnets, where the octupoles strengths were optimized to achieve an approximately uniform transverse distribution (see table 3). It can -5 - be seen that the central portion of the beam spot is uniform in both planes (∼20% of the beam), with a homogeneity of ±2% and ±4% in the x-and y-planes, respectively. The beam profiles corresponding to the target front plane, a 10 cm depth in the target, and a 20 cm depth in the target are shown in figure 7. It can be pointed out that the beam size does not increase with target depth.

Discussion on tail folding
The beam dynamics and muli-particle calculations were modeled from the LEIR extraction point to the end of the H1 beamline using the multi-particle tracking code MAD-X (Methodical Accelerator Design computer program, version X [10]). A beam of 3×10 5 particles was created using a distribution derived from the beam parameters at the LEIR extraction point.
-7 - Figure 6. Two-dimensional density distribution of the 440 MeV/u fully stripped Carbon ions beam at the target plane at the end of the H1 beamline. The beam spot is uniform over an area of 40 × 40 mm 2 (∼20% of the beam), with a beam homogeneity of ±2% in the x-plane and ±4% in the y-plane. The uniform portion of the beam spot is surrounded by two higher-intensity walls.
The higher-intensity walls outside the 40 × 40 mm 2 uniform region (see figure 6) is produced by overshot tail-folding through octupoles focusing. The beam located outside the uniform area can be collimated directly after the quadrupole triplet at the end of the H1 beamline, keeping enough space between the collimator and the target in order to limit the effect of any unwanted secondaries on the irradiated target. Another possible approach could be the idea of using dodecapole magnets instead of octupole magnets. The dodecapole magnets generate an approximately uniform transverse distribution at the target location but with the advantage of producing smaller higher-intensity walls surrounding the uniform central region [8]. Both beam options, broad beam (octupole magnets ON) and pencil beam (octupole magnets OFF), with the required specifications were obtained by adjusting the quadrupoles strengths (see table 4). One of the quadrupole converters (qh3) in the H1 beamline requires a polarity switch between pencil and broad beam optics (see table 4 (b)). More detailed studies should be carried in a next project stage to include error analysis and the design of the collimation system in front of the H1 irradiation point.

Conclusions
The first horizontal beamline (H1) employs octupole magnets to generate a uniform beam distribution at the target location. A rectangular beam area of 40 × 40 mm 2 is achieved, with a beam homogeneity of ±2% in the x-plane and ±4% in the y-plane, by adjusting the strengths of the oc-  figure 6 at the target front plane, 10 cm in target, and 20 cm in target in both x-plane (a) and y-plane (b). The beam profiles in both planes increase slightly with target depth. tupoles and quadrupoles. Such uniform irradiation fields are often necessary to irradiate biological samples (i.e. cell cultures). In addition, the H1 beam transport line is capable of providing a pencil beam with a FWHM of 4.3 mm in both planes. Furthermore, it was shown that the beam size of the broad beam does not change with target depth, which was achieved by matching the beam at the target planes and optimizing the magnets strengths.
-9 - Table 4. Maximum quadrupole gradients (G) for the common transport line and the horizontal extension H1 for both pencil and broad beams.