A conduction-cooled compact pion capture solenoid based on HTS is designed with the central field of 3 Tesla and operation temperature of 20 K to show the feasibility for the superconducting magnet applied to the future muon beam line at first-step. Likewise, the radiation influence on the thermal characteristics for the designed HTS coil is evaluated, and its thermal characteristics is very stable for 20 K design due to the peak of thermal conductivity for the thermal path as well as the high specific heat of coil. The biggest issue for the magnet can be operated under a high radiation environment is the radiation tolerance of the insulation, which should be replaced by non-organic material in the superconducting magnets for future muon beam line.
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Chapter 7 Conclusion
A conduction-cooled superconducting magnet system, COMET-PCS is designed to be operated in a high radiation environment for the high intense muon beam line. In this thesis, the irradiation influence on the thermal and quench characteristics are studied to validate the feasibility for which the conduction-cooled superconducting coils in the PCS can be operated in a high radiation environment.
In order to take the radiation influence into account, the radiation estimation is newly included into the thermal design, and the three-dimensional distribution of neutron flux and energy deposition are predicted for the thermal and quench analysis. With the experimental result of radiation damage rate on aluminum by neutron irradiation, the radiation effect is modeled as the degradation on the thermal conductivity of thermal path and stabilizer. Then, a three-dimensional thermal analysis is performed to validate the coil temperature rise during the beam operation. By employing a novel method to insert the pure aluminum strips between each layer in coils, the superconducting magnet is expected to be operated for three months at most in view of the temperature margin decrease during the beam operation, and the magnet has to be annealed before the magnet quench.
Since the radiation can also affect the electrical resistivity so that the ohmic heating can be increased during the magnet quench, a three-dimensional quench analysis is performed by using the neutron flux distribution estimated from the radiation simulation to examine the radiation influence on the quench characteristics and the effect of aluminum strips. With the helps of aluminum strips to accelerate the normal zone propagation, the maximum temperature after quench can be reduced. Then, even the hot spot temperature after quench is found to be increased due to the radiation, all of the coils in PCS is capable to be protected against quench with the aluminum strips and a by-pass dump resistor.
The thermal conductivity of BT prepreg tape is measured at cryogenic temperature, furthermore, its radiation tolerance is examined by the gamma ray irradiation with a total dose up to 5 MGy since it is found that the thermal conductivity of insulation tape affects the thermal design significantly. The measured thermal conductivity is approximately 0.02 W·m−1·K−1 at 4.5 K, and no significant degradation is observed after the gamma ray irradiation with a total dose of 0.2, 1 and 5 MGy.
At last, a conceptual design of a compact coil using a HTS is proposed as the first step to improve the thermal characteristics in a high radiation environment for future
high intense muon beam line. The study shows that the HTS coil has a good thermal stability at operation temperature of 20 K, and can be applied to the PCS in future high intense beam line with the large temperature margin.
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Appendices
Appendix A
Numerical Treatments
In this Chapter, the numerical methods utilized in the thermal and quench analysis are described, in which most of numerical methods are derived from Ref. [117]. In Sec. A.1, the Kutta-Runge method used in the calculation to solve the electrical circuit differential equation is introduced. Section A.2 describes the root finding method applied to calculate the process of current sharing at beginning of quench, including the Newton-Raphson method and secant method. Section A.3 presents the multi-dimensional linear interpolation method utilized for interpolating the magnetic field from a two-dimensional profile into the thermal and quench analysis.
A.1 Runge-Kutta Method
In quench analysis, the electrical circuit differential equation is written as the equation (5.24). Generally, it can be solved by the Euler method as
I(t)=I(t−1)− ∆t
Ltot{I(t−1)(Rdump+Rcoil) +Vd(I(t−1))} (A.1) whereI(t)is the current at present time step,I(t−1)is the current at previous time step, and
∆t is the time step, respectively. However, the Euler method gives the error of calculation if the time step is set to too large, thus an iterative method, the fourth-order Runge-Kutta method, is selected to solve the ordinary differential equations. The procedure of the numerical treatment on the fourth-order Runge-Kutta method is given as follows in quench simulation:
- The differential equation of quench protection circuit in equation (5.24) can be rearranged as
f(I, Rcoil) = dI
dt =− 1
Ltot(I(Rdump+Rcoil) +Vd(I)) (A.2) in which the differential term ofdI/dtcan be obtained by inputting the current and the coil resistance.
Appendix A. Numerical Treatments
- The iterative items are calculated until the fourth order with the time step dt and the current evaluated at previous time step I(t−1).
k1 = dt·f(I(t−1), Rcoil) k2 = dt·f(I(t−1)+ k1
2, Rcoil) k3 = dt·f(I(t−1)+ k2
2, Rcoil)
k4 = dt·f(I(t−1)+k3, Rcoil) (A.3)
- In final, the current can be calculated by I(t) =I(t−1)+k1
6 + k2 3 +k3
3 + k4
6 (A.4)