Modeling power flow in the induction cavity with a two dimensional circuit simulation

We have proposed a two dimensional (2D) circuit model of induction cavity. The oil elbow and azimuthal transmission line are modeled with one dimensional transmission line elements, while 2D transmission line elements are employed to represent the regions inward the azimuthal transmission line. The voltage waveforms obtained by 2D circuit simulation and transient electromagnetic simulation are compared, which shows satisfactory agreement. The influence of impedance mismatch on the power flow condition in the induction cavity is investigated with this 2D circuit model. The simulation results indicate that the peak value of load voltage approaches the maximum if the azimuthal transmission line roughly matches the pulse forming section. The amplitude of output transmission line voltage is strongly influenced by its impedance, but the peak value of load voltage is insensitive to the actual output transmission line impedance. When the load impedance raises, the voltage across the dummy load increases, and the pulse duration at the oil elbow inlet and insulator stack regions also slightly increase.

Figure 1

Schematic cross section of an induction cavity which mainly includes oil elbow, azimuthal transmission line, connecting tab, insulator stack, radial feed gap, cathode plate, magnetic core and output transmission line.

Figure 2

Block diagram showing the 2D circuit model topology of induction cavity. The oil elbow, azimuthal transmission line, and connecting tab are modeled with 1D transmission line elements. 2D circuit elements are used to represent the regions inward the azimuthal transmission line. The transmission line element labeled $A_1$ is used to model the oil elbow, and the elements named $B_1$ to $B_{36}$ indicate the azimuthal transmission line. The connecting tab is modeled with transmission line elements labeled $C_1$ to $C_{18}$. The insulator stack and radial feed gap regions are modeled with transmission line elements labeled $D$ to $K$ with subscript 1 to 72. The elements with subscript 1 to 36 are the azimuthal elements, and the elements with subscript 37 to 72 represent the radial elements. The transmission line elements labeled $L$ to $P$ with subscript 1 to 72 denote the output transmission line section. The elements with subscript 1 to 36 are the azimuthal elements, and the elements with subscript 37 to 72 represent the axial elements. The junctions named $X_0$ to $X_{13}$ indicate that the two junctions with the same letter are electrically connected together in the circuit model. It should be noted that this circuit model is associated with the type of connecting tab displayed in Fig. 3. The transit time of output transmission line is assumed to be 5.0 ns, and it could be easily adjusted according to the actual length of output transmission line.

Figure 3

Two examples of connecting tab configuration. (a) One continuous tab on the lower half circle allows conduction from the azimuthal transmission line to cathode plate, (b) there are two tabs on the upper half circle extending from $\pm 40$ degrees to $\pm 50$ degrees and one continuous tab on the lower half circle. The angles are measured in each direction from the midpoint of the oil elbow. The connecting tab forces the current injected onto the azimuthal transmission line to spread away from the feed port.

Figure 4

A pulse generation circuit is used to drive the 2D circuit model of induction cavity which includes Marx generator, intermediate store capacitor, laser triggered gas switch, PFL, self-breaking water switch and water transmission line. The laser triggered gas switch and self-breaking water switch are modeled with ideal elements without consideration of capacitance and resistance. The oil prepulse switch is also not taken into account. The quantities $I_C$, $C_M$, $L_M$ and $R_M$ are the equivalent charging voltage, capacitance, inductance and resistance of the Marx generator, respectively. $S1$, $S2$ and $S3$ represent the switches in the Marx generator, laser triggered gas switch and self-breaking water switch, respectively. ${\tau }_C$ and $Z_C$ are the transit time and impedance of the intermediate store capacitor, respectively. $L_{S2}$ is the inductance of laser triggered gas switch. ${\tau }_P$ and $Z_P$ are the transit time and impedance of the PFL, respectively. $L_{S3}$ is the inductance of self-breaking water switch. ${\tau }_T$ and $Z_T$ are the transit time and impedance of the water transmission line, respectively.

Figure 5

The oil elbow inlet voltage waveforms acquired by 2D circuit simulation (black solid line) and transient electromagnetic simulation (black dash-dotted line). The PFL output voltage obtained by 2D circuit simulation is also presented (black dashed line).

Figure 6

Azimuthal transmission line voltage waveforms obtained by 2D circuit simulation (black solid line) and transient electromagnetic simulation (black dash-dotted line) at (a) 0 degree, (b) 90 degrees and (c) 180 degrees.

Figure 7

Insulator stack voltage waveforms obtained by the two different methods at (a) 0 degree, (b) 90 degrees and (c) 180 degrees. The black solid line represents the results acquired by 2D circuit simulation. The black dash-dotted line represents the results acquired by transient electromagnetic simulation. The red solid line represents the result given by 1D circuit simulation. The consistency between the 2D circuit simulation results and transient electromagnetic simulation results proves the exactness of this circuit model.

Figure 8

Output transmission line and dummy load voltage waveforms acquired by 2D circuit simulation and transient electromagnetic simulation. The output transmission line voltage obtained by 1D circuit simulation (blue solid line) is also shown. The black solid line and red solid line represent the output transmission line voltage obtained by transient electromagnetic simulation and 2D circuit simulation, respectively, while the green solid line and green dash-dotted line represent the load voltage achieved by 2D circuit simulation and transient electromagnetic simulation, respectively. The output transmission line voltage probe is near the ground end. Comparing with 1D circuit simulation the output transmission line voltage waveform given by 2D circuit simulation agree with the result achieved by transient electromagnetic simulation better.

Figure 9

Load voltage waveforms obtained by 2D circuit simulation when the azimuthal transmission line impedance is 5.0, 10.0, 14.0, 20.79 and $40.0\Omega$.

Figure 10

Load voltage waveforms with different output transmission line impedance obtained by 2D circuit simulation.

Figure 11

Output transmission line voltage waveforms with different output transmission line impedance acquired by 2D circuit simulation. The voltage probe is near the ground end.

Figure 12

Load voltage waveforms with different load impedance obtained by 2D circuit simulation.

Figure 13

(a) Oil elbow inlet and (b) insulator stack voltage waveforms with different load impedance acquired by 2D circuit simulation. The insulator stack voltage probe is at 0 degrees.