Main > High Power Laser Science and Engineering >  Volume 8 >  Issue 1 >  Page 010000e8 > Article
  • Equations
  • Abstract
  • Figures (15)
  • Tables (1)
  • Equations (27)
  • References (54)
  • Get PDF
  • View Full Text
  • Paper Information
  • Received: Nov. 23, 2019

    Accepted: Feb. 7, 2020

    Posted: Mar. 27, 2020

    Published Online: Mar. 27, 2020

    The Author Email: M. J. Guardalben (mgua@lle.rochester.edu)

    DOI: 10.1017/hpl.2020.6

  • Get Citation
  • Copy Citation Text

    M. J. Guardalben, M. Barczys, B. E. Kruschwitz, M. Spilatro, L. J. Waxer, E. M. Hill. Laser-system model for enhanced operational performance and flexibility on OMEGA EP[J]. High Power Laser Science and Engineering, 2020, 8(1): 010000e8

    Download Citation

  • Category
  • Research Articles
  • Share
$$\begin{eqnarray}\displaystyle & & \displaystyle \frac{\unicode[STIX]{x1D6FF}n_{3}}{\unicode[STIX]{x1D6FF}t}=W_{p}n_{0}+c\unicode[STIX]{x1D719}\unicode[STIX]{x1D70E}_{23}n_{2}-\frac{n_{3}}{\unicode[STIX]{x1D70F}_{32}},\end{eqnarray}$$(1)

View in Article

$$\begin{eqnarray}\displaystyle & & \displaystyle \frac{\unicode[STIX]{x1D6FF}n_{2}}{\unicode[STIX]{x1D6FF}t}=c\unicode[STIX]{x1D719}\unicode[STIX]{x1D70E}_{12}n_{1}-c\unicode[STIX]{x1D719}(\unicode[STIX]{x1D70E}_{21}+\unicode[STIX]{x1D70E}_{23})n_{2}-\frac{n_{2}}{\unicode[STIX]{x1D70F}_{21}}+\frac{n_{3}}{\unicode[STIX]{x1D70F}_{32}},\qquad\end{eqnarray}$$(2)

View in Article

$$\begin{eqnarray}\displaystyle & & \displaystyle \frac{\unicode[STIX]{x1D6FF}n_{1}}{\unicode[STIX]{x1D6FF}t}=c\unicode[STIX]{x1D719}\unicode[STIX]{x1D70E}_{21}n_{2}-c\unicode[STIX]{x1D719}\unicode[STIX]{x1D70E}_{12}n_{1}+\frac{n_{2}}{\unicode[STIX]{x1D70F}_{21}}-\frac{n_{1}}{\unicode[STIX]{x1D70F}_{10}},\end{eqnarray}$$(3)

View in Article

$$\begin{eqnarray}\displaystyle & & \displaystyle \frac{\unicode[STIX]{x1D6FF}n_{0}}{\unicode[STIX]{x1D6FF}t}=-W_{p}n_{0}+\frac{n_{1}}{\unicode[STIX]{x1D70F}_{10}},\end{eqnarray}$$(4)

View in Article

$$\begin{eqnarray}\displaystyle & & \displaystyle \frac{\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D719}}{\unicode[STIX]{x1D6FF}t}+c\frac{\unicode[STIX]{x1D6FF}\unicode[STIX]{x1D719}}{\unicode[STIX]{x1D6FF}z}=c\unicode[STIX]{x1D719}(\unicode[STIX]{x1D70E}_{21}n_{2}-\unicode[STIX]{x1D70E}_{12}n_{1}-\unicode[STIX]{x1D70E}_{23}n_{2}),\end{eqnarray}$$(5)

View in Article

$$\begin{eqnarray}\displaystyle \frac{\unicode[STIX]{x1D6FF}n_{2}(z,t)}{\unicode[STIX]{x1D6FF}t} & = & \displaystyle -\frac{I(z,t)}{\hslash \unicode[STIX]{x1D714}}\unicode[STIX]{x1D70E}_{21}n_{2}(z,t),\end{eqnarray}$$(6)

View in Article

$$\begin{eqnarray}\displaystyle \frac{\unicode[STIX]{x1D6FF}I(z,t)}{\unicode[STIX]{x1D6FF}z} & = & \displaystyle I(z,t)\unicode[STIX]{x1D70E}_{21}n_{2}(z,t),\end{eqnarray}$$(7)

View in Article

$$\begin{eqnarray}G_{\text{in}}(t)=\frac{1}{1-(1-G_{0}^{-1})\exp [-F_{\text{in}}(t)/F_{\text{sat}}]}\end{eqnarray}$$(8)

View in Article

$$\begin{eqnarray}G_{\text{out}}(t)=1+(G_{0}-1)\exp [-F_{\text{out}}(t)/F_{\text{sat}}],\end{eqnarray}$$(9)

View in Article

$$\begin{eqnarray}F_{\text{sat}}=\frac{\hslash \unicode[STIX]{x1D714}}{\unicode[STIX]{x1D70E}_{21}},\end{eqnarray}$$(10)

View in Article

$$\begin{eqnarray}\displaystyle F_{\text{in}}(t)\equiv \displaystyle \int _{t_{0}}^{t}I_{\text{in}}(t^{\prime })\,\text{d}t^{\prime }, & & \displaystyle\end{eqnarray}$$(11)

View in Article

$$\begin{eqnarray}\displaystyle F_{\text{out}}(t)\equiv \displaystyle \int _{t_{0}}^{t}I_{\text{out}}(t^{\prime })\,\text{d}t^{\prime }. & & \displaystyle\end{eqnarray}$$(12)

View in Article

$$\begin{eqnarray}I_{\text{out}}(t)=G_{\text{in}}(t)I_{\text{in}}(t),\end{eqnarray}$$(13)

View in Article

$$\begin{eqnarray}I_{\text{in}}(t)=I_{\text{out}}(t)/G_{\text{out}}(t).\end{eqnarray}$$(14)

View in Article

$$\begin{eqnarray}I_{k}(t,x,y)=\unicode[STIX]{x1D6FD}^{2}\cdot G_{k}(t,x,y)I_{k-1}(t,x,y),\end{eqnarray}$$(15)

View in Article

$$\begin{eqnarray}\displaystyle & & \displaystyle \hspace{-18.0pt}G_{k}(t,x,y)\nonumber\\ \displaystyle & & \displaystyle \hspace{-12.0pt}\quad =\frac{1}{1-\{1-[G_{0}(x,y)]^{-1}\}\exp [-F_{k}(t,x,y)/F_{\text{sat}}]},\end{eqnarray}$$(16)

View in Article

$$\begin{eqnarray}\displaystyle & & \displaystyle \hspace{-18.0pt}F_{k}(t,x,y)=\displaystyle \int _{t_{0}}^{t}\unicode[STIX]{x1D6FD}\cdot I_{k-1}(t^{\prime },x,y)\,\text{d}t^{\prime },\end{eqnarray}$$(17)

View in Article

$$\begin{eqnarray}\displaystyle I_{k}(t,x,y) & = & \displaystyle I_{k+1}(t,x,y)/\unicode[STIX]{x1D6FD}^{2}\cdot G_{k}(t,x,y),\end{eqnarray}$$(18)

View in Article

$$\begin{eqnarray}\displaystyle G_{k}(t,x,y) & = & \displaystyle 1+[G_{0}(x,y)-1]\exp [-F_{k}(t,x,y)/F_{\text{sat}}],\nonumber\\ \displaystyle & & \displaystyle\end{eqnarray}$$(19)

View in Article

$$\begin{eqnarray}\displaystyle F_{k}(t,x,y) & = & \displaystyle \displaystyle \int _{t_{0}}^{t}[I_{k+1}(t^{\prime },x,y)/\unicode[STIX]{x1D6FD}]\text{d}t^{\prime },\end{eqnarray}$$(20)

View in Article

$$\begin{eqnarray}F_{\text{sat}}^{\prime }=\frac{\hslash \unicode[STIX]{x1D714}/\unicode[STIX]{x1D70E}_{\text{em}}}{\unicode[STIX]{x1D6FE}(R)},\end{eqnarray}$$(21)

View in Article

$$\begin{eqnarray}\unicode[STIX]{x1D6FE}(R)=1+K\cdot B(R)\end{eqnarray}$$(22)

View in Article

$$\begin{eqnarray}G_{0}(x,y)=\left\{\frac{[F_{\text{out}}(x,y)/F_{\text{in}}(x,y)]_{\text{pumped}}}{[F_{\text{out}}(x,y)/F_{\text{in}}(x,y)]_{\text{unpumped}}}\right\}^{1/N},\end{eqnarray}$$(23)

View in Article

$$\begin{eqnarray}\displaystyle & & \displaystyle G_{k}(t,x,y)\nonumber\\ \displaystyle & & \displaystyle =\frac{1}{1-\{1-[\unicode[STIX]{x1D6FC}\cdot G_{0}(x,y)]^{-1}\}\exp [-F_{k}(t,x,y)/F_{\text{sat},k}(x,y)]},\nonumber\\ \displaystyle & & \displaystyle\end{eqnarray}$$(24)

View in Article

$$\begin{eqnarray}F_{\text{sat},k}(x,y)=\frac{m\displaystyle \int _{-\infty }^{\infty }\unicode[STIX]{x1D6FD}\cdot I_{k-1}(t,x,y)\,\text{d}t+b}{\unicode[STIX]{x1D6FE}(R)},\end{eqnarray}$$(25)

View in Article

$$\begin{eqnarray}\displaystyle G_{k}(t,x,y) & = & \displaystyle 1+[\unicode[STIX]{x1D6FC}\cdot G_{0}(x,y)-1]\nonumber\\ \displaystyle & & \displaystyle \times \,\exp [-F_{k}(t,x,y)/F_{\text{sat},\text{k}}(x,y)],\end{eqnarray}$$(26)

View in Article

$$\begin{eqnarray}F_{\text{sat},k}(x,y)=\frac{m\displaystyle \int _{-\infty }^{\infty }[I_{k+1}(t,x,y)/\unicode[STIX]{x1D6FD}]\text{d}t+b}{\unicode[STIX]{x1D6FE}(R)}.\end{eqnarray}$$(27)

View in Article

Please Enter Your Email: