Transverse emittance measurement for the Heavy Ion Medical Machine cyclotron

ACCELERATOR, RAY TECHNOLOGY AND APPLICATIONS

Transverse emittance measurement for the Heavy Ion Medical Machine cyclotron

Yong-Chun Feng，

Min Li，

Rui-Shi Mao，

Bing Wang，

Sheng-Peng Li，

Wei-Long Li，

Wei-Nian Ma，

Xin-Cai Kang，

Jin-Quan Zhang，

Peng Li，

Tie-Cheng Zhao，

Zhi-Guo Xu，

You-Jin Yuan

Nuclear Science and Techniques

Vol.30, No.12

Article number 184

Published in print 01 Dec 2019

Available online 22 Nov 2019

DOI：10.1007/s41365-019-0699-7

47003

The transverse emittance of the extracted beam from the Heavy Ion Medical Machine cyclotron is measured and then optimized for injection into the synchrotron. For the purposes of cross validation, three methods, i.e., slit-grid, Q-scan, and 3-grid, are used to measure the emittance. In the slit-grid technique, an automatic selection of the region of interest is adopted to isolate the major noise from the beam phase space, which is an improvement over the traditional technique. After iterating over the contour level, an unbiased measurement of the emittance can be obtained. An improvement of the thin lens technique is implemented in the Q-scan method. The results of these measurements are presented.

Heavy Ion Medical MachineTransverse emittanceSlit-grid

1 Introduction

The Heavy Ion Medical Machine (HIMM) developed by the Institute of Modern Physics is now undergoing a clinical trial [1, 2]. It consists of two Electron Cyclotron Resonance (ECR) ion sources, a cyclotron, and a synchrotron that has a compact structure with a circumference of 56.2 m. The feedback-based slow-extraction technique [3] is adopted to deliver a high-quality beam spill into five treatment terminals. The layout of the HIMM complex is shown in Fig. 1. The cyclotron is critical for optimized injection into the synchrotron. The HIMM cyclotron is an isochronous machine with four magnet sectors and two RF-gap Dees that accelerate ¹²C⁵⁺ to approximately 7 MeV/u. The extracted beam intensity is up to 10 μA in Continuous Wave (CW) mode. Preliminary calculations indicate that the emittance containing 95% of beam particles is up to 60 mm mrad. Up to now, the slow-extraction efficiency has reached nearly 90% for all energies from 120 to 400 MeV/u. The spill duty factor has exceeded 90% at a sample rate of 10 kHz [4].

Fig. 1.

The layout of the HIMM complex.

Emittance is one of the critical beam parameters for accelerators that reveal the beam quality directly. The definitions of phase space and emittance are well documented in Refs. [5, 6]. The most commonly used methods to extract the emittance include the slit-grid [7, 8], pepper-pot [9-11], Quadrupole-scan (Q-scan) [12-14], and 3-grid [13, 15] techniques. During the commissioning phase of a newly designed machine, the slit-grid and pepper-pot techniques are the standard methods used to display the intensity distribution of a phase space with an arbitrary shape. Aberrations and filamentation induced by mismatch, higher-order effects of the beam optics as well as space-charge effects can then be investigated in a straightforward manner [16]. However, the pepper-pot must be calibrated very carefully using extremely parallel light before a reliable result is obtained, so we do not make use of this method in this study.

Before integrating the cyclotron into the HIMM complex, a dedicated beam line has been constructed temporarily at the Institute of Modern Physics (IMP), and the emittance measurements are performed along it. In this paper, the measurements of the transverse emittance using the three methods mentioned above are discussed, and the automatic selection technique of the Region Of Interest (ROI) is described in detail.

2 Experimental setup

The diagnostics beam line is located at the exit of the cyclotron, as shown in Fig. 2. Two pairs of slits(SL) are employed to perform the slit-grid measurement. Four Multi-Wire (MW) monitors are used to sample the beam profile and also perform the 3-grid measurement. The distance between these devices is calibrated using a FARO Laser Tracker, and the position coordinates are summarized in Table 1. Each MW has a sensitive area of 47 mm×47 mm, which corresponds to 47 wires for both the horizontal and vertical directions with a gap of 1 mm and a diameter of 0.2 mm. The readouts for the x and y directions are separate, so the measurement can be conducted for both planes simultaneously. Each pair of slits scans the beam for its corresponding plane. Both of the slits are driven by a Servo Motor with positioning precision better than 1 μm. Along the beam line, two Faraday Cups (FCs) are installed. FC1 is located before the entrance of MW1, and FC2 is at the end of the beam line. Both of the FCs can be used to measure beam intensity. FC2, however, acts as the beam dump and is, therefore, always kept inside the beam line. FC1 is used to block the beam while the MW is pushed into the beam pipe center, which can protect the MW electronics against radiation damage. During the measurement, it is removed from the beam line.

Position coordinates of the slits and MWs

Device	SL1/SL2	SL3/SL4	MW1	MW2	MW3	MW4
Position (mm)	2451.2	2611.4	2929.85	4001.1	5123.6	5280.7

Fig. 2.

Beam diagnostics layout.

To reduce the thermal loading of the MW, a chopper upstream of the cyclotron is powered on during the emittance measurement, which decreases the CW current to 1 μA. The data acquisition system is based on NI’s CompactRIO controller, which runs on a real-time system with a reaction time of less than 1 ms and has a fast calculation ability [17]. A LabVIEW-based routine is developed to control the motion of the motors and acquire MW profile information. The collected data are firstly stored on disk, and then a Python-based post-processing script is employed for further analysis. The data length is determined by the sample time, and the average thereof over the total data gives a more reliable measurement.

3 Emittance measurement

3.1 Slit-grid technique

In a low-energy heavy ion machine, the slit-grid technique is one of the most widely used methods for emittance diagnostics. In this method, a small slit opening selects the beamlet at that position, and an MW located downstream samples the distribution and reveals the divergence of the beamlet. By scanning the slit across the beam cross section, the whole phase space can be obtained, which generates a two-dimensional (2D) data matrix that is just the area used in the emittance calculation. Thus, the emittance can be retrieved statistically according to the algorithm given in Ref. [18].

(1)

In this way, the Root Mean Square (RMS) emittance and TWISS parameters can be evaluated by

\begin{array}{l} ε_{x} = σ_{x} σ_{x^{'}} \sqrt{1 - ρ^{2}} \\ β = \frac{σ_{x}}{σ_{x^{'}}} \frac{1}{\sqrt{1 - ρ^{2}}} \\ γ = \frac{σ_{x^{'}}}{σ_{x}} \frac{1}{\sqrt{1 - ρ^{2}}} \\ α = - ρ \sqrt{β γ} \end{array}

(2)

where $I_{n_{x}, n_{x^{'}}}$ represents the entries of the data matrix, nx and nx’ are the total number of rows and columns, which correspond to the scan number and wire number, respectively. Area elements ΔxΔx’ are determined by the step width of the slit and the gap of the MW and are defined by Δx=(x_max-x_min)/nx and $Δ x^{'} = ({x^{'}}_{max} - {x^{'}}_{min}) / n_{x^{'}}$ . X₀ and $X_{0^{'}}$ give the center of the matrix.

Typically, the data is noisy owing to disturbances from the MW electronics and the environment. It is, therefore, necessary to denoise the data before performing the calculation using Equation 2. In this paper, we use a systematic procedure to complete the emittance evaluation. The three steps to perform the image denoising are discussed below.

Interpolation

An ad hoc-based interpolation is implemented along a specified axis, upon which the phase space distribution can be refined, and therefore the density of the area elements is increased. The interpolation can significantly improve the smoothness of the image because the noise typically has a white Gaussian distribution with a zero mean. Moreover, interpolation can compensate for the roughness of the sparsely sampled phase space.

Wavelet denoising

The 2D matrix array is denoised using a BayesShrink-based wavelet threshold denoising algorithm [19], which tends to result in an overly smooth image compared to that obtained with a single threshold. The wavelet denoising algorithm consists of three steps: 1) Applying the wavelet transform. This transformation decomposes the noisy image into different frequency sub-bands and generates a series of wavelet coefficients, 2) Applying a thresholding method. There exist various algorithms estimating the threshold, such as VisuShrink, SureShrink, NormalShrink, and BayesShrink. The BayesShrink algorithm is an adaptive approach to wavelet soft thresholding where a unique threshold is estimated for each wavelet sub-band [19], which is more effective in removing Gaussian noise[20], and 3) Reconstructing the image. By adopting the inverse wavelet transformation, the denoised image can be recovered.

ROI selection

The Marching Squares-based edge detection algorithm [21] is adopted to mask an ROI, which is the area containing only the good data. The Marching Squares algorithm is a special case of the Marching Cubes algorithm, which generates contours for a two-dimensional scalar field. In reality, a series of contour lines is generated, the number of which depends strongly on the contour level. Typically, it is desirable to select the biggest one as the ROI. The next step is to set the signal outside the ROI to zero and keep the inside, which will be further denoised, unchanged. While continuing to repeat the operation with an increased contour level, a curve can be generated that gives the trend of the emittance against the contour level. By fitting the smooth part of the curve with a line and extrapolating to the position at which the contour level is zero, the unbiased estimation of the emittance can be obtained. The remarkable advantage of this algorithm compared to the typical global denoising algorithms is the isolation of the major noise from the ROI, e.g., wire damage. In addition, the automatic selection of the ROI is also a significant improvement to the unbiased emittance evaluation.

A virtual simulated measurement is then conducted, which is done to benchmark the proposed algorithm. In this simulation, the user-specified beam parameters as well as the associated noise distribution are given to generate the noisy beam. A virtual slit with an adjustable opening samples the beamlet, and a grid downstream collects the particle hits on the wire. The simulation parameters used are summarized in Table 2, where Q_len is the quadrupole length, and D is the drift length. Figure 3 shows the noisy and reconstructed phase space. It is obvious that the signal-to-noise ratio is significantly improved after interpolation, wavelet denoising, and ROI selection have been implemented. The measured 1 σ ellipse matches the actual version well except that the tail is shorter than expected, which can be explained by the long tail of the Gaussian distribution being smeared by the noise and then cut out by the threshold. The obtained emittance as a function of threshold is shown in the upper panel of Fig. 4. A linear fit is applied to the region that has a constant derivative, and extrapolation is performed to obtain the "real" emittance with a zero threshold. The measured emittance is consistent with the specified value. The quantized error decreases with the increased interpolation number as shown in the lower panel of Fig. 4, and a deviation of below 4% is reached when interpolation number 4 is given.

Simulation parameters

Parameter	є_rms(μ m)	β (m)	α (rad)	E_k (MeV/u)	ion	Q_len (m)	D (m)
Value	5	37	6	0.26	¹²C⁶⁺	0.4	2.38

Fig. 3.

Reconstructed phase space using the beam parameters listed in Table 1 with a slit gap of 1 mm, a slit step of 1 mm, a wire gap of 1 mm, a wire diameter of 0.1 mm, and a drift length of 1.5 m. Upper panel: noisy distribution; lower panel: denoised and marked phase. space.

Fig. 4.

Upper panel: the emittance evolution against the threshold; lower panel: the error of the reconstructed emittance against the interpolation number.

In this measurement scheme, SL1&SL2, SL3&SL4, and MW4 are employed to perform measurements of the horizontal and vertical planes. The distance between the slit and the MW is 2.8295 m and 2.6692 m for the horizontal and vertical planes, respectively, which results in an angle resolution of 0.353 mrad and 0.375 mrad, respectively, based on the definition Δx’=(d_wire+2r_wire)/L, where d_wire is the gap between the wires, r_wire is the diameter of the wire, and L is the distance. The aperture of the slit for both of the planes is set to 1 mm, which is identical to the MW spacing, and the slit stepping length is also 1 mm, so the whole phase plane can be scanned without overlapping.

The raw data are averaged over the whole sample length to cancel the random noise preliminarily. The initial and denoised phase spaces are shown in the upper panels of Fig. 5 and Fig. 6 for the horizontal and vertical planes, respectively. A significant difference is observed when the denoising procedure described above is implemented. The contour line defines the beam boundary precisely. The measured 95% emittance is 45.32 mm mrad and 37.56 mm mrad for the horizontal and vertical planes, respectively.

Fig. 5.

(Color online) The horizontal phase space and emittance evaluation. Upper panel: the raw phase space (top) and the denoised phase space (bottom). The red dashed line is the contour line with a contour level of 10%, and the black dashed line is the measured 1 σ phase ellipse. Lower panel: the emittance evolution under the various contour levels.

Fig. 6.

(Color online) The vertical phase space and emittance evaluation. Upper panel: the raw phase space (top) and the denoised phase space (bottom). The red dashed line is the contour line with a contour level of 15%, and the black dashed line is the measured 1 σ phase ellipse. Lower panel: the emittance evolution under the various contour levels.

3.2 Q-scan technique

For a beam line with low intensity, like the diagnostics line of the HIMM cyclotron, the space-charge effects can be negligible; hence, the Q-scan technique is suitable for emittance measurements. If the focus length of the lens is larger than the length of the lens itself, a thin lens approximation can be adopted. The most frequently used case is a quadrupole followed by a drift section. Thus, the squared profile width at the MW is a quadratic function of the quadrupole gradient. Quite often, for a thin lens approximation, the thick lens is assumed to have zero length while keeping the strength constant. In this paper, we introduce a new method to split the thick lens into one thin lens plus two drift sections, which is the first-order approximation of the thick lens, and the conjugate of the three elements satisfies the symplectic condition. The schematic is shown in Fig. 7.

Fig. 7.

Thick lens split

Without the loss of generality, the transfer matrix of a thick lens can be expressed as

M_{thick} = [\begin{matrix} C & S \\ C^{'} & S^{'} \end{matrix}]

(3)

According to the split method mentioned above, the matrix can thus be written equivalently as M_thick = M_drift1M_thinM_drift2, where

\begin{array}{l} M_{drift1} = [\begin{matrix} 1 & L_{1} \\ 0 & 1 \end{matrix}] \\ M_{thin} = [\begin{matrix} 1 & 0 \\ - K & 1 \end{matrix}] \\ M_{drift2} = [\begin{matrix} 1 & L_{2} \\ 0 & 1 \end{matrix}] \end{array}

(4)

If we assume L₁=L₂=L/2, the following equation will be obtained

K = - C^{'}, \frac{L}{2} = \frac{C - 1}{C^{'}}

(5)

The evolution of L/2 with respect to quadrupole strength is illustrated in Fig. 8. Since the change of the half-length with quadrupole current is sufficiently small, the average over the scan current gives a better substitution. Therefore, the effective drift length now becomes 〈L/2〉+ D with D being the original distance from the quadrupole exit to the MW. Evidently, this split method represents the thick lens more reliably.

Fig. 8.

The change of the effective magnet vs. the quadrupole current.

The actual energy is measured based on three phase probes along the beam line, and this gives the measurement value of 6.323 MeV/u, which is slightly different from the theoretical value. The magnet calibration curve is given by B’=0.01347+0.0219I_Q, where I_Q is the quadrupole current. The quadrupole length is 0.35 m; thus, the quadrupole strength can be calculated by $K = | \frac{B^{'}}{B ρ} | L$ with Bρ=0.871Tm. The profile data for each step of the quadrupole scan is averaged over the sample length, and a parabolic fit is performed. The algorithm is identical to that in Ref. [22]. The measurement data and fit process are shown in Fig. 9. The measured 95% emittance is 51.5 mm mrad and 31.8 mm mrad for the horizontal and vertical planes, respectively.

Fig. 9.

(Color online) Q-scan data and parabolic fit. Upper panel: the horizontal plane; lower panel: the vertical plane.

3.3 3-grid technique

In this measurement, MW1, MW2, and MW3 are used to sample the profile. The emittance can thus be retrieved uniquely by virtue of a parabolic fit or by solving the following linear equations directly.

[\begin{matrix} σ_{11} (0) \\ σ_{12} (0) \\ σ_{22} (0) \end{matrix}] = {[\begin{matrix} 1 & 2 L_{1} & L_{1}^{2} \\ 1 & 2 L_{2} & L_{2}^{2} \\ 1 & 2 L_{3} & L_{3}^{2} \end{matrix}]}^{- 1} [\begin{matrix} σ_{11} (1) \\ σ_{11} (2) \\ σ_{11} (3) \end{matrix}]

(6)

Both methods give identical results as expected. The measurement data and fit process are shown in Fig. 10. The measured 95% emittance is 56.93 mm mrad and 38.15 mm mrad for the horizontal and vertical planes, respectively.

Fig. 10.

(Color online) 3-grid data and parabolic fit. Upper panel: the horizontal plane; lower panel: the vertical plane.

4 Summary

In this study, the emittance at the exit of the HIMM cyclotron was measured using three methods. The slit-grid algorithm was improved by introducing the automatic selection of an ROI, and a satisfactory result was obtained. For the Q-scan method, an optimized thin lens approximation algorithm was implemented, which gave a more reliable result. As presented in Table 3, the results of these measurements agree with one another for the vertical plane. There is a discrepancy for the horizontal plane, however. Based on our preliminary deductions, this is attributed to the non-zero dispersion contribution. The dispersion and its derivative are -1.77 m and -0.66 rad in the horizontal plane at the exit of cyclotron, respectively, and the temporal beam line is not designed to be dispersion-free in the diagnostics section.

Measurement results

Methods	Slit-grid	Q-scan	3-grid
Horizontal(95%) [mm mrad]	45.32	51.5	56.93
Vertical(95%) [mm mrad]	37.56	31.8	38.15

References

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