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  • Received: Dec. 7, 2019

    Accepted: Mar. 10, 2020

    Posted: Jun. 9, 2020

    Published Online: Jun. 9, 2020

    The Author Email: Fabrizio Consoli (fabrizio.consoli@enea.it)

    DOI: 10.1017/hpl.2020.13

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    Fabrizio Consoli, Vladimir T. Tikhonchuk, Matthieu Bardon, Philip Bradford, David C. Carroll, Jakub Cikhardt, Mattia Cipriani, Robert J. Clarke, Thomas E. Cowan, Colin N. Danson, Riccardo De Angelis, Massimo De Marco, Jean-Luc Dubois, Bertrand Etchessahar, Alejandro Laso Garcia, David I. Hillier, Ales Honsa, Weiman Jiang, Viliam Kmetik, Josef Krása, Yutong Li, Frédéric Lubrano, Paul McKenna, Josefine Metzkes-Ng, Alexandre Poyé, Irene Prencipe, Piotr Ra̧czka, Roland A. Smith, Roman Vrana, Nigel C. Woolsey, Egle Zemaityte, Yihang Zhang, Zhe Zhang, Bernhard Zielbauer, David Neely. Laser produced electromagnetic pulses: generation, detection and mitigation[J]. High Power Laser Science and Engineering, 2020, 8(2): 02000e22

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$$\begin{eqnarray}T_{h}\simeq (\unicode[STIX]{x1D6FE}_{0}-1)m_{e}c^{2},\end{eqnarray}$$(1)

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$$\begin{eqnarray}P_{E}=\frac{\unicode[STIX]{x1D707}_{0}}{6\unicode[STIX]{x1D70B}c}|\ddot{D}|^{2},\end{eqnarray}$$(2)

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$$\begin{eqnarray}{\mathcal{E}}_{\text{THz}}\simeq \frac{Z_{0}}{6\unicode[STIX]{x1D70B}t_{\text{ej}}}Q_{e}^{2}\,\simeq \frac{Q_{e}^{2}}{1.5\unicode[STIX]{x1D70B}C_{t}},\end{eqnarray}$$(3)

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$$\begin{eqnarray}P_{E}=\frac{2.44}{8\unicode[STIX]{x1D70B}}Z_{0}|J_{\unicode[STIX]{x1D714}_{s}}|^{2}.\end{eqnarray}$$(4)

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$$\begin{eqnarray}{\mathcal{E}}_{\text{GHz}}\simeq \frac{2.44c}{32\unicode[STIX]{x1D70B}l_{s}}Z_{0}Q_{e}^{2}N_{h}\simeq 0.1\frac{c}{d_{t}}Z_{0}Q_{e}^{2}.\end{eqnarray}$$(5)

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$$\begin{eqnarray}\unicode[STIX]{x2202}_{t}f_{eh}=S_{\text{las}}(\unicode[STIX]{x1D700},t)-\unicode[STIX]{x1D70F}_{ee}^{-1}f_{eh}-g_{e}(\unicode[STIX]{x1D700},t),\end{eqnarray}$$(6)

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$$\begin{eqnarray}\unicode[STIX]{x1D719}_{E}(t)=\frac{1}{2\unicode[STIX]{x1D70B}\unicode[STIX]{x1D716}_{0}}\int _{0}^{t}\text{d}t^{\prime }\frac{J_{e}(t^{\prime })}{R_{e}(t^{\prime })+c(t-t^{\prime })}.\end{eqnarray}$$(7)

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$$\begin{eqnarray}\unicode[STIX]{x1D719}_{E}(t)=\frac{1}{2\unicode[STIX]{x1D70B}\unicode[STIX]{x1D716}_{0}}\int _{0}^{t}\text{d}t^{\prime }\frac{J_{e}(t^{\prime })-J_{n}(t^{\prime })}{R_{e}(t^{\prime })+c(t-t^{\prime })}.\end{eqnarray}$$(8)

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$$\begin{eqnarray}\displaystyle \begin{array}{@{}c@{}}\mathbf{E}=\displaystyle \mathop{\sum }_{i=1}^{+\infty }A_{i}\mathbf{E}_{i}+\displaystyle \mathop{\sum }_{i=1}^{M-1}A_{i}^{0}\mathbf{E}_{i}^{\,0}+\displaystyle \mathop{\sum }_{i=1}^{+\infty }B_{i}\mathbf{s}_{i},\\ \mathbf{H}=\displaystyle \mathop{\sum }_{i=1}^{+\infty }C_{i}\mathbf{H}_{i}+\displaystyle \mathop{\sum }_{i=1}^{P-1}C_{i}^{\,0}\mathbf{H}_{i}^{\,0}+\displaystyle \mathop{\sum }_{i=1}^{+\infty }D_{i}\mathbf{g}_{i},\end{array} & & \displaystyle\end{eqnarray}$$(9)

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$$\begin{eqnarray}\text{AE}(t)\equiv \left|x(t)+\frac{i}{\unicode[STIX]{x1D70B}}\text{PV}\int _{-\infty }^{+\infty }\frac{x(\unicode[STIX]{x1D70F})}{t-\unicode[STIX]{x1D70F}}\,\text{d}\unicode[STIX]{x1D70F}\right|,\end{eqnarray}$$(10)

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$$\begin{eqnarray}f(t)=A_{0}\left[\exp \left(-\frac{t}{\unicode[STIX]{x1D70F}_{f}}\right)-\exp \left(-\frac{t}{\unicode[STIX]{x1D70F}_{r}}\right)\right]\,u(t).\end{eqnarray}$$(11)

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$$\begin{eqnarray}F_{x}^{w}(t,f)\equiv \int _{-\infty }^{+\infty }x(\unicode[STIX]{x1D70F})w(\unicode[STIX]{x1D70F}-t)e^{-2\unicode[STIX]{x1D70B}if\unicode[STIX]{x1D70F}}\,\text{d}\unicode[STIX]{x1D70F},\end{eqnarray}$$(12)

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$$\begin{eqnarray}S_{x}^{w}(t,f)\equiv \left|F_{s}^{w}(t,f)\right|^{2}.\end{eqnarray}$$(13)

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$$\begin{eqnarray}\mathbf{E}=-c~\hat{\mathbf{n}}\times \mathbf{B},\quad \mathbf{B}=c^{-1}~\hat{\mathbf{n}}\times \mathbf{E},\end{eqnarray}$$(14)

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$$\begin{eqnarray}\displaystyle s_{3}(t) & = & \displaystyle s_{2}(t)+n_{1}(t)+n_{2}(t)+n_{3}(t)+n_{4}(t)\nonumber\\ \displaystyle & = & \displaystyle h_{\text{TL}}(t)\circledast \left[s_{0}(t)+n_{0}(t)\right]+n_{\text{ext}}(t),\end{eqnarray}$$(15)

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$$\begin{eqnarray}s_{2}(t)+{\mathcal{F}}^{-1}\{H_{\text{TL}}^{-1}N_{\text{ext}}\}(t)={\mathcal{F}}^{-1}\{H_{\text{TL}}^{-1}S_{3}\}(t),\end{eqnarray}$$(16)

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$$\begin{eqnarray}\unicode[STIX]{x1D6FC}=2\unicode[STIX]{x1D70B}\sqrt{\unicode[STIX]{x1D706}_{c}^{-2}-\unicode[STIX]{x1D706}^{-2}},\end{eqnarray}$$(17)

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$$\begin{eqnarray}G\{\mathbf{L}(s)\}=\frac{sK_{A}\mathbf{L}(s)\cdot A_{\text{eq}}}{1+s\unicode[STIX]{x1D70F}}=\frac{sK_{l}\mathbf{L}(s)\cdot l_{\text{eq}}}{1+s\unicode[STIX]{x1D70F}}\end{eqnarray}$$(18)

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$$\begin{eqnarray}V_{0}=ZA_{\text{eq}}\,\text{d}B/\text{d}t,\end{eqnarray}$$(19)

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$$\begin{eqnarray}\oint _{S}\mathbf{B}\cdot \text{d}\mathbf{s}=\unicode[STIX]{x1D707}_{0}J_{n},\end{eqnarray}$$(20)

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$$\begin{eqnarray}J_{n}=-\frac{1}{L}\int V_{0}\left(t\right)\,\text{d}t,\end{eqnarray}$$(21)

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$$\begin{eqnarray}n_{e}/n_{\text{at}}=1-\exp (-\unicode[STIX]{x1D70E}_{\text{ph}}F_{\text{ph}}),\end{eqnarray}$$(22)

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$$\begin{eqnarray}\text{SE}=k\log (f/2cl_{a})\,[\text{dB}],\end{eqnarray}$$(23)

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