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Chinese Physics B
Vol. 29, Issue 10, (2020)

Modes decomposition in particle-in-cell software CEMPIC

Aiping Fang^1,2,†, Shanshan Liang¹, Yongdong Li³, Hongguang Wang^3,4, and Yue Wang^3,4

Author Affiliations

¹School of Physics, Xi’an Jiaotong University, Xi’an 70049, China

²State Key Laboratory of Intense Pulsed Radiation Simulation and Effect (Northwest Institute of Nuclear Technology), Xi’an 71004, China

³Key Laboratory for Physical Electronics and Devices of the Ministry of Education, School of Electronic and Information Engineering, Xi’an Jiaotong University, Xi’an 710049, China

⁴Xian Moduo Technology Co., Ltd, Xi’an 71009, China

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DOI: 10.1088/1674-1056/abaed6 Cite this Article

Aiping Fang, Shanshan Liang, Yongdong Li, Hongguang Wang, Yue Wang. Modes decomposition in particle-in-cell software CEMPIC[J]. Chinese Physics B, 2020, 29(10): Copy Citation Text

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Abstract

The numerical method of modes analysis and decomposition of the output signal in 3D electromagnetic particle-in-cell simulation is presented. By the method, multiple modes can be resolved at one time using a set of diagnostic data, the amplitudes and the phases of the specified modes can all be given separately. Based on the method, the output signals of one X-band tri-bend mode converter used for one high power microwave device, with ionization process in the device due to the strong normal electric field, are analyzed and decomposed.

Keywords

high power microwave device mode decomposition particle-in-cell tri-bend mode converter

\begin{array}{r} \overset{⌢}{e_{i}} = \int_{L_{i}} \boldsymbol E (\boldsymbol r, t) \cdot d \boldsymbol l, {\overset{⌢}{\overset{⌢}{b}}}_{i} = \int_{S_{i}} \boldsymbol B (\boldsymbol r, t) \cdot d \boldsymbol s, \end{array}

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\begin{array}{r} \overset{⌢}{h_{i}} = \int_{{\tilde{L}}_{i}} \boldsymbol H (\boldsymbol r, t) \cdot d \boldsymbol l, {\overset{⌢}{\overset{⌢}{d}}}_{i} = \int_{{\tilde{S}}_{i}} \boldsymbol D (\boldsymbol r, t) \cdot d \boldsymbol s, \end{array}

(2)

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\begin{array}{r} \begin{array}{ll} \overset{⌢}{\boldsymbol e} = {(\begin{array}{cccccc} \overset{⌢}{e_{1}} & \overset{⌢}{e_{2}} & \dots & \overset{⌢}{e_{i}} & \dots & \overset{⌢}{e_{N}} \end{array})}^{T}, \\ \overset{⌢}{\boldsymbol h} = {(\begin{array}{cccccc} \overset{⌢}{h_{1}} & \overset{⌢}{h_{2}} & \dots & \overset{⌢}{h_{i}} & \dots & \overset{⌢}{h_{N^{^{'}}}} \end{array})}^{T}, \end{array} \end{array}

(3)

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\begin{array}{r} \begin{array}{c} \overset{⌢}{\overset{⌢}{\boldsymbol d}} = {(\begin{array}{cccccc} {\overset{⌢}{\overset{⌢}{d}}}_{1} & {\overset{⌢}{\overset{⌢}{d}}}_{2} & \dots & {\overset{⌢}{\overset{⌢}{d}}}_{i} & \dots & {\overset{⌢}{\overset{⌢}{d}}}_{N} \end{array})}^{T}, \\ \overset{⌢}{\overset{⌢}{\boldsymbol b}} = {(\begin{array}{cccccc} {\overset{⌢}{\overset{⌢}{b}}}_{1} & {\overset{⌢}{\overset{⌢}{b}}}_{2} & \dots & {\overset{⌢}{\overset{⌢}{b}}}_{i} & \dots & {\overset{⌢}{\overset{⌢}{b}}}_{N^{^{'}}} \end{array})}^{T}, \end{array} \end{array}

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\begin{array}{r} \overset{⌢}{\overset{⌢}{\boldsymbol d}} = {\boldsymbol M}_{ε} \overset{⌢}{\boldsymbol e}, \overset{⌢}{\overset{⌢}{\boldsymbol b}} = {\boldsymbol M}_{μ} \overset{⌢}{\boldsymbol h}, \end{array}

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\begin{array}{r} \begin{array}{ll} {\boldsymbol M}_{μ}^{- 1} \boldsymbol C \overset{⌢}{\boldsymbol e} = - \frac{d}{d t} \overset{⌢}{\boldsymbol h}, \end{array} \end{array}

(6)

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\begin{array}{r} \begin{array}{ll} {\boldsymbol M}_{ε}^{- 1} \tilde{\boldsymbol C} \overset{⌢}{\boldsymbol h} = \frac{d}{d t} \overset{⌢}{\boldsymbol e}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} {\boldsymbol M}_{ε}^{- 1} \tilde{\boldsymbol C} {\boldsymbol M}_{μ}^{- 1} \boldsymbol C \overset{⌢}{\boldsymbol e} = - \frac{d^{2}}{d t^{2}} \overset{⌢}{\boldsymbol e}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} {\boldsymbol M}_{μ}^{- 1} \boldsymbol C {\boldsymbol M}_{ε}^{- 1} \tilde{\boldsymbol C} \overset{⌢}{\boldsymbol h} = - \frac{d^{2}}{d t^{2}} \overset{⌢}{\boldsymbol h} . \end{array} \end{array}

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\begin{array}{r} \boldsymbol A \overset{⌢}{\boldsymbol e} = ω^{2} \overset{⌢}{\boldsymbol e}, \end{array}

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\begin{array}{r} \tilde{\boldsymbol A} \overset{⌢}{\boldsymbol h} = ω^{2} \overset{⌢}{\boldsymbol h}, \end{array}

(11)

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\begin{array}{r} {\boldsymbol e}_{i} \cdot {\boldsymbol e}_{j} = {\begin{cases} 0, & i \neq j, \\ 1, & i = j, \end{cases} \end{array}

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\begin{array}{r} {\boldsymbol h}_{i} \cdot {\boldsymbol h}_{j} = {\begin{cases} 0, & i \neq j, \\ 1, & i = j . \end{cases} \end{array}

(13)

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\begin{array}{r} \boldsymbol Q = \sum_{j} {\boldsymbol q}_{j}, \end{array}

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\begin{array}{r} {\boldsymbol q}_{j} = \cos (k_{j} z - ω t + ϕ_{j}^{+}) {\boldsymbol A}_{j}^{+} + \cos (k_{j} z - ω t + ϕ_{j}^{-}) {\boldsymbol A}_{j}^{-}, \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{1} = & \cos (k_{j} z_{1} - ω t_{1} + ϕ_{j}^{+}) A_{j}^{+} \\ + \cos (k_{j} z_{1} - ω t_{1} + ϕ_{j}^{-}) A_{j}^{-}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{2} = & \cos (k_{j} z_{2} - ω t_{2} + ϕ_{j}^{+}) A_{j}^{+} \\ + \cos (k_{j} z_{2} - ω t_{2} + ϕ_{j}^{-}) A_{j}^{-}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{3} = & \cos (k_{j} z_{3} - ω t_{3} + ϕ_{j}^{+}) A_{j}^{+} \\ + \cos (k_{j} z_{3} - ω t_{3} + ϕ_{j}^{-}) A_{j}^{-}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{4} = & \cos (k_{j} z_{4} - ω t_{4} + ϕ_{j}^{+}) A_{j}^{+} \\ + \cos (k_{j} z_{4} - ω t_{4} + ϕ_{j}^{-}) A_{j}^{-} . \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} z_{2} = z_{1} + \frac{1}{4} \frac{2 π}{k}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} z_{3} = z_{1}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} z_{4} = z_{1} - \frac{1}{4} \frac{2 π}{k}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} t_{2} = t_{1}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} t_{3} = t_{4} = t_{1} - \frac{1}{t} \frac{2 π}{ω}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{1} = \cos (ψ_{j}^{+}) A_{j}^{+} + \cos (ψ_{j}^{-}) A_{j}^{-}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{2} = \cos (ψ_{j}^{+} + ϕ_{j}^{0}) A_{j}^{+} + \cos (ψ_{j}^{-} + ϕ_{j}^{0}) A_{j}^{-}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{3} = \sin (ψ_{j}^{+}) A_{j}^{+} + \sin (ψ_{j}^{-}) A_{j}^{-}, \end{array} \end{array}

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\begin{array}{r} \begin{array}{ll} q_{j}^{4} = - \sin (ψ_{j}^{+} - ϕ_{j}^{0}) A_{j}^{+} + \sin (ψ_{j}^{-} - ϕ_{j}^{0}) A_{j}^{-} . \end{array} \end{array}

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\begin{array}{r} \begin{array}{c} A_{j}^{+} = \frac{\sqrt{{(q_{j}^{1} \cos ϕ_{j}^{0} - q_{j}^{2} - q_{j}^{3} \sin ϕ_{j}^{0})}^{2} + {(- q_{j}^{3} \cos ϕ_{j}^{0} + q_{j}^{4} + q_{j}^{1} \sin ϕ_{j}^{0})}^{2}}}{2 \sin ϕ_{j}^{0}}, \end{array} \end{array}

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\begin{array}{r} A_{j}^{-} = \frac{\sqrt{{(q_{j}^{1} \cos ϕ_{j}^{0} - q_{j}^{2} + q_{j}^{3} \sin ϕ_{j}^{0})}^{2} + {(- q_{j}^{3} \cos ϕ_{j}^{0} + q_{j}^{4} - q_{j}^{1} \sin ϕ_{j}^{0})}^{2}}}{2 \sin ϕ_{j}^{0}} . \end{array}

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Aiping Fang, Shanshan Liang, Yongdong Li, Hongguang Wang, Yue Wang. Modes decomposition in particle-in-cell software CEMPIC[J]. Chinese Physics B, 2020, 29(10):

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