2.1 Mechanical design and control system upgrades

The upper panel of Fig. 2 shows the mechanical design of the vertical (left picture) and new horizontal (right picture) IPMs. Obviously, a few mechanical features and changes are listed as follows.

Fig. 2.Full-screen View

(Color online) The IPM sketch and control system, in which the panel (a) shows the vertical IPM with some 100 mega-ohm resistors for the field shaping, (b) is the new compact design of horizontal IPM with separate HV supplies, and (c) is an EPICS control system showing the raw image of beams and the processed profile data.

·The clearance between the upper and lower plates is approximately 170 mm in the vertical IPM, while it is compactly designed only 120 mm for the new IPM. Undoubtedly, a shorter clearance will result in less time used for the signal ions’ drift and consequently higher profile measurement accuracy. In case of blocking the beams, this dimension can only be properly reduced to a certain extent.

·The number of the bias electrodes is 18 in the vertical IPM for the field shaping, but it is designed only 8 for the new IPM due to a larger surface of each electrode parallel to the electric field direction. This change is beneficial not only to reduce the number of the bias electrodes needed, but also to maintain the uniformity of the electric field.

·Instead of circular MCPs applied in the former vertical IPM, the new IPM uses rectangular MCPs for the advantage of a larger effective area. In addition, the insulator material of MCPs relating to the thermal baking and the vacuum outgassing should be carefully chosen.

·To avoid the possible resistors deterioration during a harsh thermal baking, the new IPM uses separate electrodes for each bias voltage supply rather than by means of the tandem resistors. This change will surely increase the costs of HV channels, but it makes the voltage values on each of the IPM electrodes controllable and precise.

Some delicate material and surface treatments are demanded during the new IPM manufacture. At first, the 316L type stainless steel and the 99% aluminium oxide ceramic are both pre-treated inside a 900 degree Celsius furnace for the surface outgassing. Then in order to prevent some microscopic protuberances discharging, all the metallic electrodes are carefully processed by the ultrasonic cleaning, the surface polishing, and the edge grinding as well. Moreover, all the connection points between the insulator ceramic and metallic electrodes are carefully designed to avoid any surface discontinuity, which is especially important on the inner surface of the bias electrodes to form an uniform electric field.

The optics system is simply designed by setting the camera directly after a quartz view window for a large numerical aperture. As for the high radiation case, an optical fiber or a long distance reflective light path may be needed for the sake of the camera protection. Generally, the spatial uncertainty from the two-layer MCPs is approximately 3 times the pore spacing of 12 μm, thus the spatial resolution of the whole optics system calibrated around 63 μm per pixel seems convincing and reliable. A 4.2 mega-pixel scientific Complementary Metal–Oxide–Semiconductor (sCMOS) chip is connected with two Camera Link (CL) cables for the digital data transmission. The response frequency of this sCMOS camera has been tested up to 100 frames per second with the full pixel resolution.

The former IPM utilizes a commercial software to control the camera with no data processing function. As shown in the lower panel of Fig. 2, a new IPM control system has been developed based on the Experimental Physics and Industrial Control System (EPICS), which easily accomplishes many useful features including the Region Of Interest (ROI) selection, the profile data fitting and the historical profile display, etc. It also can be triggered by a nearby DC current transformer (DCCT) to simultaneously store the transverse profile and beam current data. The whole system eventually achieves approximately 200 ms time delay with the exception of the camera exposure time, which is much slower than the camera response time of 10 ms. This is mainly because of the profile data processed via the EPICS Process Variables (PVs), and a faster way is to process the massive image data by a Field-Programmable Gate Array (FPGA) hardware.

2.2 Initial signal yield evaluation

An evaluation about the initial signal yield is essential for the IPM design, especially for the application cases under the ultra-high vacuum condition in a synchrotron. In theory, the Coulomb collision mostly occurs between the charged beam particles and the orbit electrons of residual gas molecules, thus the energy loss also can be regarded as the electric stopping power in gas targets. The electric stopping power can be described by the well-known Bethe formula in Eq. (1) [5].

where N_A is the Avogadro number, m_e and r_e are the mass and the classical radius of the electron, z_p is the nuclear charge of an incident particle, Z_t and A_t are the atomic number and the nuclear mass of the target, the residual gas density can be calculated by the state equation of ideal gas ρ_t=PA_t/RT with gas pressure P, temperature T and ideal gas constant R, βc and γ are the velocity and the relativistic factor of the incident particle, I is the mean excitation/ionization potential of gas targets, β² inside the bracket represents a relativistic correction term. In the energy range of 0.05≤βγ≤1000, the Bethe formula gives a good approximation to the energy loss of heavy particles within a few percent.

Some experimental data of the ionization energy for general residual gases are shown in Table 1 [6]. Subsequently, the energy loss from a single beam particle traversing through gas targets can be calculated in Eq. (1), and by another well-known code named SRIM [7] as well. Substituting the beam parameters of Kr³⁰⁺ with energy 422 MeV/u at 293.15 K and the main gas species of H₂ with 810^-10 Pa pressure in HIRFL-CSRm. The calculated energy loss is 2.2910^-14 MeV/mm in Eq. (1), and 2.1810^-14 MeV/mm by the SRIM code.

The calculation results actually indicate that the energy loss transferred to the residual gas targets is actually negligible compared to the beam kinetic energy. In addition, the results of the two calculation methods will have less discrepancy when the incident particle is a light ion like the proton. The Bethe formula treats the incident particle as a bare nuclei with the atomic charge z_p by default, while the SRIM code uses an effective charge state instead. Generally, the energy loss of heavy ions calculated by the SRIM are quite identical to those experimental data within a mean error of 8.90% [7].

The energy loss for a single beam particle traveling through residual gas targets is solved. Subsequently, the final signal photons reaching the camera chip can be approximately evaluated in Eq. (2).

where N_p means the number of beam particles per bunch, M is the magnification and transmission factor for the optics system, G is the gain of the MCPs, F means an average quantum efficiency of the phosphor screen and the camera chip, t is the integration/exposure time of the camera, f_r=βc/C means the revolution frequency and C=161 m is the circumference of HIRFL-CSRm.

Substituting the energy loss of 2.18×10^-14 MeV/mm by the SRIM code, f_r and N_p are determined by the kinetic energy 422 MeV/u and the beam current 1.5 mA in the normal operation mode of HIRFL-CSRm, the two-layer MCPs with a "V" style channel combination are chosen for a high gain G of 10⁶ and an effective length L of 30 mm, the phosphor screen and the camera chip totally attain an average quantum efficiency F around 50%, which actually varies with different photon wavelengths, the factor M relating to the solid angle and the lens material is roughly calculated approximately 10^-3 for our optics system. Eventually, the total photon yield arriving at the camera chip is approximately 2.05×10³ only for a turn of the beam passage, and 2.76×10⁷ for the camera exposure time of 10 ms, both of which are enough for the detectable sensitivity of the sCMOS chip used. As a result, though the residual gas pressure is extremely low as 8×10^-10 Pa, the new IPM would successfully work at HIRFL-CSRm.

2.3 Some considerations about residual gas

In fact, the residual gas used for the IPM detection should be regarded as a compound gas target. The gas composition is excepted to be 85% of H₂, and 15% of N₂ or CO in HIRFL-CSR [1]. In this case, an accurate stopping power can be calculated by S_c=∑fiSi, where fi and Si are the mass percentage and the stopping power of each element. Compared with the lightest gas species H₂, a heavier gas molecule will result in larger electric stopping power and consequently more ion-electron pairs acting as the IPM signals.

The residual gas pressure is positively proportional to the IPM signal amplitude, but it only slightly influences the beam width by changing the signal to noise ratio and the statistical error from the profile data. Compared with the camera exposure time, only a fast changing of the gas pressure can notably affect the beam size fitted by the IPM data. The most probable speed of ideal gas molecules based on a Maxwell-Boltzmann distribution is $v=\sqrt{2k_{\text{B}}T/\pi m}$, with molecular mass m, temperature T, and Boltzmann constant k_B. For an average nuclear mass of 18.7 for a compound gas target at 293.15 K, the velocity is calculated approximately 288 m/s. Consequently, the time it takes molecules to reach a nearby pump is much longer than the ionization and capture events. Therefore, the global pressure may be considered constant with respect to the camera exposure time. As for the local pressure variation, the previous research indicates a parabolic pressure distribution between the two pumps surrounding an IPM. And the pressure difference between the pressure gauge and the IPM location is no larger than 7% [8].

The residual gas molecules depleted by the IPM also can be roughly assessed. Based on the state equation of ideal gas n=pV/RT, the detectable volume within the new IPM is approximately 648 cm³ resulting in about 1.2810⁸ gas molecules capable of producing measurable particles. However according to Eq. (2), the created residual gas ions is calculated approximately 5.5210⁴ for the camera exposure time of 10 ms, being only 0.043% of the total gas molecules inside the IPM working volume. Furthermore, the gas molecules actually can be supplemented by the beam induced desorption from the pipe walls [8]. Unfortunately, the precise measurements for both the local pressure variation and the residual gas depletion can not be done at the HIRFL-CSRm IPM site.

2.4 Space charge and initial momentum analysis

Three major factors still could negatively affect the IPM measurement accuracy, which are the initial velocity of signal particles, the non-uniformity of the electric field and the space charge field from intense beams. In theory, the most of the energy transfer goes into the electrons since the electron mass is small. Therefore, the initial velocity of gas ions mainly appears as the thermal motion of gas molecules and it hardly causes the position deviation during the whole drift journey. For a non-uniform beam distribution in HIRFL-CSRm, the impact of the space charge field on the signal gas ions can be approximatively calculated in Eq. (3) [9].

where I_B is the beam current, ε₀ is the vacuum permittivity, σ is the rms size for a Gaussian distribution beam, and r represents the distance from the beam center. Substituting the cooled beam parameters of Kr³⁰⁺ with energy 422 MeV/u, current 1.5 mA and σ=1 mm, E_em calculated at $r=\sqrt{2}\sigma$ shows a relatively large value of 26.38 V/m. The potential difference of 6 kV between a 120 mm clearance attains a field strength around 510⁴ V/m. Thus, the space charge field is actually negligible compared to the electric field under the HIRFL-CSRm beam conditions.

Additionally, a systematic simulation integrating the initial momentum and the space charge effect can be done by some lab-developed codes [10]. The upper panel of Fig. 3 shows a space charge field Ex as a function of the horizontal position. The value of |Ex| reaches 28 V/m at maximum, which agrees well with the calculation result in Eq. (3).

Fig. 3.Full-screen View

(Color online) IPM Simulations by a lab-developed code named IPMsim3D [10]. The upper panel depicts a space charge field Ex as a function of the horizontal position. The value of |Ex| reaches 28 V/m at maximum. The lower panel shows the initial and tracked particles’ counting rate as a function of the horizontal position. The fitted profile sizes are σr=1.49 mm for the initial particles and σt=1.48 mm for the tracked particles, respectively.

The lower panel of Fig. 3 shows the initial and tracked particles’ counting rate as a function of the horizontal position. The fitted profile sizes are σi=1.49 mm for the initial particles and σ_t=1.48 mm for the tracked particles, respectively. The particle-tracking simulation indicates a broadening profile measurement error of +0.68% caused by the space charge of beams and the initial momentum of signal particles.

2.5 Simulations and beam experiments about electric field

It turns out that the major inaccuracy of the IPM profile measurement is caused by the electric field non-uniformity. Some commercial codes are capable of evaluating the field distribution and performing particle-tracking simulations. It is also feasible to import the three-dimensional field data into the lab-developed code [10] for an overall assessment.

In fact due to the presence of gaps and holes in the IPM structure, the real field distribution even varies with different high voltage (HV) settings. It is reasonable that different HV values applied on the IPM electrodes results in a small change of the field shape. Now IPMs in the world are mainly set with two HV types on the upper and lower plates: symmetric bipolar HV setting (± 5 kV for example), and asymmetric unipolar HV setting (10 kV and ground level for example).

In order to explore the impact of different HV settings on the IPM properties, both commercial code simulations and beam experiments are done under three different HV setups shown in Table 2. Five critical IPM electrodes shown in Fig. 2 are set with different voltage combinations. Compared with the potential difference of 6 kV in the HV setup B and C, the setup A has a smaller value of 4 kV just in consideration of a redundant protection for the MCPs.

Figure 4 presents the field distributions simulated by a commercial code using the finite integration technique. Firstly, the electric field near the metallic chamber surface are reasonably distorted to satisfy the electric boundary condition. The equipotential lines in the upper panel of setup A are actually quite straight inside the IPM central region, which indicates a very flat and uniform vertical field Ey there. Near the MCPs area, the equipotential lines are deformed due to the mechanical breach and gaps. As a result, this curved shape of the electric field probably enlarges the profile projection on the sensor of IPM. By comparison, the lower panel of setup C shows an inversely curved field along all the drift path of signal particles, which most likely shrinks the signal ions’ footprint on the MCPs. The electric field of setup B is not shown here, because it is very similar to that of the setup C (less curved).

Fig. 4.Full-screen View

(Color online) The electric field distribution as a function of different HV setups. The upper panel of setup A shows that the equipotential lines are quite flat in the central region, but obviously curved near the MCPs. The lower panel of setup C shows an inversely curved field inside all the IPM working region. The field distribution of setup B is not shown here, because it is very similar to that of the setup C (less curved).

Figure 5 shows the particle-tracking simulations under different HV settings shown in Table 2. An obvious linearity between the initial and detected particles’ position has been found for all the three HV setups, which actually means a constant field distortion along the horizontal direction (x). In addition, a good field consistency in the longitudinal (z) and vertical (y) directions is also validated by changing the initial particle’s coordinate along the two directions. The data slope of three tracking results reveal that the HV setup A has a broadening profile measurement error of +1.50%, which probably results from the specific and curved field near the MCPs, also see the upper panel of Fig. 4. The setup B and C reflect a focusing error of -7.50% and -15.60% respectively, because both fields show an inversely curved shape compared to that of the setup A.

Fig. 5.Full-screen View

(Color online) The tracked particle position as a function of the initial particle position. The setup A shows that the tacked particle position is a little larger than that of the initial, having a small and broadening error of +1.50%. However, the setup B and C indicate a focusing error of -7.50% and -15.60%, respectively.

Figure 6 depicts two obvious bi-gaussian profiles for the beams cooled enough to reach an equilibrium state in HIRFL-CSRm. In theory, the smallest transverse emittance should stay unchanged under the same cooling condition. As shown in Eq. (4), this ultimate beam size is mainly determined by the tune shift resulting from the increase of the space charge during the beam cooling [11].

Fig. 6.Full-screen View

(Color online) Intensity as a function of the horizontal position. The setup C apparently measures a smaller beam size and the measured beam center is closer to the geometric center compared to that of the setup A. The profile data of setup B is not shown due to its strange asymmetric distribution in the longitudinal direction, details see the next subsection.

where βx is the transverse betatron function, N=I/(Zef_r) means the number of beam particles per bunch, $l_{\text{b}}=C/(2\sqrt{\pi })$ and R=C/(2π) with the circumference of C=161 m, r_i=(Ze)²/AM is the classical ion radius, the experimental data of Δv=0.10.2 [11] means the maximum tune shift caused by the beam cooling. Substituting the injected beam parameters of Kr²⁸⁺ with energy 4.98 MeV/u, current 125 μA and βx=15 mm at the new IPM site, eventually an equilibrium beam size is calculated σx=1.62∼2.29 mm. This rough calculation gives a possible range for the cooled beam size in HIRFL-CSRm as a theoretical benchmark.

Figure 6 shows that the new IPM indeed measures two different beam profiles as a consequence of different HV settings. This can only be explained that the electric field of the HV setup C focuses the signal ions more strongly than that of the setup A. And this focusing field even moves the whole signal ions’ projection to the geometric center of the new IPM. Apparently, the beam size of setup C is smaller than that of the setup A with a relative error of -16.68%, which is quite identical to the simulated error difference of -17.10% shown in Fig. 5. The profile measurements show a very good agreement with the simulations of the commercial software. Consequently, some data corrections could be added to precisely retrieve the real beam size and it is particularly necessary for the IPM applications in intense beams.

The former vertical IPM has been benchmarked with a wire scanner in SSC-Linac and it measures a beam size approximately 8.8% smaller than that of the wire scanner [4]. This measurement error mainly comes from the deformity of the electric field, because the space charge effect there is also negligible and the profile measurements are very identical to the field simulations. Unfortunately due to the space limitation at HIRFL-CSRm, the new horizontal IPM can not be checked by another profile instrument.

In conclusion, the symmetric HV setup A achieves more uniform field distribution compared to asymmetric ones like the setup B and C, but it brings more challenges for the MCPs’ insulation and operation, especially for the IPM applications under the ultra-high voltage setup.

2.6 Operational cautions and experimental anomalies

One unusual phenomenon should be paid attention to during the IPM operation. When the two-layer MCPs are supplied with the same polarity HV channels, the lower MCP will be affected by some induced voltages and consequently the voltage feedback reading is always improper. As a result, the gain of the MCPs becomes much lower than the value expected and the risk of discharging between the two MCPs also rises. This problem possibly results from the HV board defect or the unreal high resistance between the two MCPs. And fortunately, it can be avoided by using the opposite polarity channels for the two-layer MCPs.

Another unexpected behavior of the phosphor screen flashing during the beam operation happened only once at HIRFL-CSRm. With the aid of an interceptive scintillator screen, the reason for this anomaly is excluded for the P46 defect and eventually it is found to be a small malfunction of the magnet current.

Also as shown in Fig. 7, the new IPM measures an asymmetric profile distribution along the longitudinal direction, but the simulations show no evidence to explain it. A similar phenomenon also occurred in the Jülich IPM [12] and the cause was deduced to be the defect of the phosphor screen. During our IPM experiments, this anomaly disappears and even repeats again as long as the IPM voltages change between the setup B and C. Therefore, this phenomenon probably results from the zero potential difference between the lower plate and the upper MCP. Most likely, it is the improper HV setting making the MCPs vulnerable for the secondary particles’ impact or possible partial field deformity forming. More experiments are needed to further study this issue.

Fig. 7.Full-screen View

(Color online) Raw profile images observed by the IPMs. The left upper panel of setup B shows an asymmetric profile along the longitudinal direction, while the left lower panel of setup C obtains a normal profile distribution. The right panel from the Jülich IPM also presents a similar asymmetry [12]. The raw image of setup A is not shown here because it is very similar to that of the setup C. In all pictures, the light extension orientation is exactly the longitudinal direction of the beam propagation.