High-precision high-voltage detuning system for HIAF-SRing electron target

Abstract

The development of a detuning system for the precision control of electron energy is a major challenge when electron targets are used in ion-storage rings. Thus, a high-precision, high-voltage, detuning system was developed for the electron target of a high-intensity heavy-ion accelerator facility-spectrometer ring (HIAF-SRing) to produce accurate electron–ion relative energies during experiments. The system consists of auxiliary, and high-voltage detuning power supplies. The front stage of the auxiliary power supply adopts an LCC resonant converter operating in the soft-switching state and an LC filter for a sinusoidal waveform output in the post-stage. The detuning power supply is a high-voltage pulse amplifier (HVPA) connected with a high-voltage DC (HVDC) module in series. In this paper, the design and development of the detuning system are described in detail, and the test bench is presented. The test results demonstrated that the detuning system conforms to the technical specifications of the dielectronic recombination (DR) experiment. Finally, a Fe¹⁵⁺ DR spectrum was measured using the detuning system. The experimental data demonstrated a good experimental resolution and verified the reliability and feasibility of the design.

Appendix

The components a, c, and e used in the imaginary transfer function calculation described in Eq. (1) were obtained using the following formula:

$$\begin{gathered} a = L_{1} L_{2} L_{3} C_{1} C_{2} C_{3} \hfill \\ c = L_{2} L_{3} C_{2} C_{3} + C_{1} C_{3} L_{1} L_{3} + C_{1} C_{2} \left( {L_{1} L_{3} + L_{2} L_{3} + L_{1} L_{2} } \right) \hfill \\ e = L_{2} C_{2} + L_{3} C_{3} + C_{2} L_{3} + L_{1} C_{1} + L_{3} C_{1} \hfill \\ \end{gathered}$$

(20)

The components φ₁, φ_2, and φ₃ used in formula (11) can be obtained by the following:

$$\begin{gathered} \varphi_{1} = U_{i} \sin w_{0} T_\text{s} \hfill \\ \varphi_{2} = U_\text{i} (1 + \cos w_{0} T_\text{s} ) \hfill \\ \varphi_{3} = \frac{{\varphi_{2} + (C_{1} //C_{3} )\sqrt {L_{1} } \sin w_{0} T_\text{s} }}{{C_{3} \sqrt {C_{1} //C_{3} } }} + \frac{{\sqrt {L_{1} } i_\text{L} }}{{2C_{1} \sqrt {C_{1} //C_{3} } }} \hfill \\ \end{gathered}$$

(21)

The components $A_{1} ,A_{2} ,B_{1} ,B_{2} ,C_{1} ,C_{2} ,D_{1} ,D_{2} ,E_{1}$, and $E_{2}$ in the transfer function of the equivalent detuning power supply described in Eq. (17) are obtained by the following formula:

$$\begin{aligned} A_{1} = & R_{1} R_{2} R_{4} R_{5} C_{2} C_{B} L_{B} C_{i} \hfill \\ B_{1} = & (R_{1} R_{2} R_{4} + R_{2} R_{4} R_{5} - R_{1} R_{3} R_{5} )C_{B} L_{B} C_{i} \hfill \\ \, &+R_{1} R_{2} R_{4} R_{5} C_{2} C_{B} (R_{B} C_{i} + L_{B} R_{p} ) \hfill \\ C_{1} = & R_{1} R_{2} R_{4} R_{5} C_{2} (C_{B} R_{B} R_{p} + C_{i} ) + (C_{B} R_{B} C_{i} + C_{B} L_{B} R_{p} ) \hfill \\ \, & (R_{1} R_{2} R_{4} + R_{2} R_{4} R_{5} - R_{1} R_{3} R_{5} ) \hfill \\ D_{1} = & R_{1} R_{2} R_{4} R_{5} C_{2} R_{p} + (R_{1} R_{2} R_{4} + R_{2} R_{4} R_{5} - R_{1} R_{3} R_{5} ) \hfill \\ \, & (C_{B} R_{B} R_{p} + C_{i} ) \hfill \\ E_{1} = & (R_{1} R_{2} R_{4} + R_{2} R_{4} R_{5} - R_{1} R_{3} R_{5} )R_{p} \hfill \\ A_{2} = & R_{1} C_{2} C_{B} L_{B} C_{g} C_{L} R_{B} \hfill \\ B_{2} = & R_{1} C_{2} (C_{L} + C_{g} )C_{B} R_{B} + C_{B} L_{B} C_{g} C_{L} R_{B} \hfill \\ C_{2} = & (C_{L} + C_{g} )C_{B} L_{B} + R_{1} C_{2} R_{B} \left( {C_{g} C_{L} + (C_{L} + C_{g} )C_{B} } \right) \hfill \\ D_{2} = & R_{1} C_{2} (C_{L} + C_{g} ) + C_{g} C_{L} R_{B} + (C_{L} + C_{g} )C_{B} R_{B} \hfill \\ E_{2} = & C_{L} + C_{g} \hfill \\ \end{aligned}$$

(22)

$$kT_{||} = \frac{{(kT_\text{c} )^{2} }}{{2E_\text{kin} }} + C\frac{{e^{2} }}{{4\pi \varepsilon_{0} }}n_\text{e}^{\frac{1}{3}} + \frac{{E_\text{kin} }}{\gamma + 1}\left(\frac{\Delta U}{U}\right)^{2}$$

(23)