Estimation of the Anode Power Supply Current of the J-PARC MR RF system for 1.36s cycle operation

The J-PARC Main Ring (MR) delivers high-intensity proton beams for the neutrino experiment. The beam intensity delivered to the neutrino experiment reached 520kW with a cycle time of 2.48 seconds in 2021. We chose to shorten the MR cycle time to 1.36 seconds to achieve higher beam intensity. An anode power supply feeds a high-voltage DC current to the tetrode vacuum tubes, which drive the RF cavity. Beam acceleration in a shorter MR cycle requires a higher RF voltage to keep the RF bucket large enough and a larger anode power supply current for the beam loading compensation. We plan to add RF systems to achieve higher RF voltage and to manage the output current of each anode power supply under limitations. To estimate the anode power supply current with a shorter MR cycle, we derived the beam loading compensation contribution in the power supply current using the data recorded during the operation with a cycle time of 2.48 seconds. We present the estimated anode power supply current for various combinations of RF voltage and the number of RF cavities.


Introduction
The Main Ring synchrotron (MR) [1] in the Japan Proton Accelerator Research Complex (J-PARC) [2] is a high-intensity proton synchrotron that accelerates protons from 3 GeV to 30 GeV.The MR delivers the proton beams to the neutrino experiment by fast extraction (FX).The output beam power delivered to the neutrino experiment reached 520kW, corresponding to 2.7 × 10 14 protons per pulse (ppp) with a cycle time of 2.48 seconds in 2021.
Towards the future beam power of 1.3 MW for the Hyper Kamiokande experiment, we selected a 2-stage upgrade plan for the MR [3].The increase in beam power will be achieved by a higher repetition cycle and more protons per pulse.The repetition cycle will be shortened to 1.36 s with a shortened acceleration time of 650 ms from 2023 and to 1.16 s with a shortened acceleration time of 580 ms from 2025.

Upgrade scenario for MR RF system
To accelerate more protons in a shorter repetition cycle, a higher acceleration voltage is required for the RF system to keep the RF buckets large enough.We plan to add more RF systems for acceleration [4,5].Two RF systems were installed between 2020 and 2023 to achieve acceleration with V RF = 510 kV by nine cavities.Two more RF systems will be installed between 2023 and 2025 to achieve acceleration with V RF = 600 kV by eleven cavities.Figure 1 shows the RF voltage V RF and the beam synchronous phase φ s for various operation cycle times of the MR.Both V RF and φ s are increased in a faster operation cycle.In addition to the higher RF voltage, the RF system requires more current to compensate for the increased beam loading caused by higher intensity beams.An anode power supply (anode PS or APS) supplies high voltage DC current to the tetrode vacuum tubes that drive the RF cavity.An APS consists of 15 inverter units and has a peak current limit of 110 A. Since the APS output current is expected to exceed the current limit of the current APS at 1.3 MW operation, we plan to modify the APS to store four more inverters to extend the current limit and allow an output current of more than 130 A. [4,5].

Anode PS output current analysis
To estimate the APS output current for various beam intensities with a shorter MR cycle, we analyzed the APS output current waveform recorded during the operation with a cycle time of 2.48 seconds.

Relationship between APS output current and beam current
To estimate the APS output current for various beam intensities, it is necessary to derive the contribution of the beam load compensation to the APS output current.From the phasor diagram, the real and imaginary components of I g can be described as follows:

Analysis of the APS output current data
The APS output current waveforms for various beam intensities recorded in 2021 are used as the data for the APS output current with the operation cycle of 2.48 s.The APS waveform was recorded with an oscilloscope at a sampling rate of 5 kHz.

Estimation for 1.36 s cycle operation
The APS current at the end of acceleration in 1.36 s cycle operation can be estimated by using Eq.1 with changing I 0 and φ b to account for the change in V RF and φ s as shown in Fig. 1.Since V RF increases for a shorter operation cycle, the current to generate the RF voltage for a single cavity, I 0 , also increases linearly with V RF .
In the case of the 1.36 s cycle operation, the RF voltage at the end of the acceleration is 510 kV with nine cavities, and φ s increases from 25 • to 30 • .Since the number of RF cavities also increases from 7 to 9, the increase in RF voltage per single RF cavity is a factor of 510/256 ×7/9=1.55.
Figure 5 shows the estimated APS output current for the MR cycle of 1.36 s in the case of seven or nine RF cavities with V RF of 510 kV.Considering a ∼5A variation in the APS output current, the operational limit on the APS output current for the 15-unit APS configuration is 105 A. Under this limit, a maximum beam intensity of 2.6×10 14 ppp can be achieved in both cases.After modifying the APS for the 19-unit configuration, the APS current limit increases to 133 A and a maximum beam intensity of 3.3×10 14 ppp can be achieved.

Summary
Beam acceleration with a shorter repetition cycle is key to the J-PARC MR upgrade scenario for increasing beam power.A shorter acceleration time requires a higher RF voltage and a higher APS output current.To estimate the APS output current for MR operation with a 1.36 s cycle, the relationship between the APS output current and the beam power is obtained by analyzing the measured APS output current waveform.From the estimation, a maximum beam intensity of 2.6×10 14 ppp can be achieved in 1.36 s cycle operation for the APS with 15 inverter units.After modifying the APS to store 19 inverter units, a maximum beam intensity of 3.3×10 14 ppp can be achieved in 1.36 s cycle operation.

Figure 1 .
Figure 1.Pattern of the RF voltage V RF and the beam synchronous phase φ s for various operation cycle of the MR.

Figure 2 .
Figure 2. Phasor diagram for currents fed into an RF cavity.

Figure 2
Figure2shows a phasor diagram of various currents fed into the RF cavity.In the case of the RF cavity of the MR for acceleration, only the harmonic component of h = 9 is mainly driven by a tetrode tube, and only beam loading compensation is performed for other harmonic components such as h = 6 ∼ 8, 10 ∼ 12. Thus, this figure represents the relationship between the generator current from a tetrode tube and the beam current for the h = 9 harmonic component.I g and I b represent the generator current from the tetrode tube and the beam current, respectively.I t = I g + I b represents the current supplied to the RF cavity.φ z represents the cavity detuning angle.I t is required to have a real component I 0 = I t cos φ z large enough to generate the RF voltage for acceleration.To keep I t and I 0 the same, a larger I g is required for a larger I b .From the phasor diagram, the real and imaginary components of I g can be described as follows:

I 0 1 + Y sin φ b cos φ g + I neighbor = I 0 1 +
φ b , where Y = I b /I 0 represents the relative beam loading factor.Assuming that the APS output current for driving the h = 9 component increases linearly with the I g , the total APS output 14th International Particle Accelerator Conference Journal of Physics: Conference Series 2687 (2024) 052022 IOP Publishing doi:10.1088/1742-6596/2687/5/0520224 current I p can be described as: I p ∝ I g + I neighbor = Re(I g )/ cos φ g + I neighbor = Y sin φ b cos arctan(− tan φz−Y cos φ b 1+Y sin φ b ) + I neighbor , where I neighbor represents the APS output current used for the beam loading compensation of the harmonic components other than h = 9.Assuming that both I neighbor and Y increase linearly along with the beam intensity P , I neighbor and Y can be written as I neighbor = nP, Y = yP , and I p can be expressed as a function of beam intensities P : I p (P ) = I 0 1 + yP sin φ b cos arctan(− tan φz−yP cos φ b 1+y sin φ b ) + nP (1) φ z can be derived from the impedance measurement of the RF cavity, and I 0 can be derived from the APS current measurement without beam(P = 0, φ b = 0 • ).The parameters n, y can be obtained by fitting the PS output current data at time with various beam phases for various beam intensities.

Figure 3
Figure3shows a typical waveform of the APS output current in the case of a beam intensity of 2.56 × 10 14 ppp (495 kW).Since the waveform fluctuates around ± 5 A(σ ∼1.3 A), the 100sample moving average smoothed waveform is used to obtain typical APS current values.The

Figure 4 .
Figure 4. APS output current at the end of acceleration for various beam intensities.

Figure 4
Figure 4 shows the measured and estimated APS output current at the end of acceleration for various beam intensities in the case of MR with the operation cycle of 2.48 sec.The anode PS output current value of the smoothed waveform at t = 1.44 s and t = 1.53 s are used as the APS output current data points with φ s = 25 • and 0 • , respectively.The RF voltage is the same for both timings, and the total voltage of 7 cavities is 256 kV.The data points of Fig.4 are fitted with Eq.1.The fitted curves fit well for data with φ s = 25 • and 0 • .

Figure 5 .
Figure 5.Estimated APS output current for MR cycle of 1.36 s.

Table 1 .
Upgrade scenario of the J-PARC MR parameter