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The accelerator itself is a tunnel 10 units long 2 units wide and 2 units high. The cross-section of the accelerator is formed by a semicircular arch on a rectangle. 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0.27266 lineto 0.54444 0.27468 lineto 0.54211 0.27649 lineto 0.54 0.27812 lineto stroke 1.5 -0.30902 moveto 1 0 lineto 0.83333 0.10301 lineto 0.75 0.15451 lineto 0.7 0.18541 lineto 0.66667 0.20601 lineto 0.64286 0.22073 lineto 0.625 0.23176 lineto 0.61111 0.24035 lineto 0.6 0.24721 lineto 0.59091 0.25283 lineto 0.58333 0.25751 lineto 0.57692 0.26148 lineto 0.57143 0.26487 lineto 0.56667 0.26781 lineto 0.5625 0.27039 lineto 0.55882 0.27266 lineto 0.55556 0.27468 lineto 0.55263 0.27649 lineto 0.55 0.27812 lineto stroke grestore % End of Graphics MathPictureEnd :[font = text; inactive; preserveAspect; ] Accelerator Tunnel :[font = text; inactive; preserveAspect; ] The equations governing the acceleration of an electron by a constant electric field can be solved exactly. The position x, the observer's time t, and the § value are given in terms of the electron's proper time tau: x = c*tau0*(Cosh[tau/tau0] - 1) t = tau0*Sinh[tau/tau0] § = Tanh[tau/tau0] where tau0 = m*c/(e*E) In our example we choose to have § = .99 at the end of the tunnel (x =10). :[font = input; preserveAspect; startGroup; ] tauovrtau0max = ArcTanh[.99] :[font = output; output; inactive; preserveAspect; endGroup; ] 2.646652412362246198 ;[o] 2.64665 :[font = input; preserveAspect; startGroup; ] ctau0 = 10/(Cosh[tauovrtau0max]-1) :[font = output; output; inactive; preserveAspect; endGroup; ] 1.642356492160584064 ;[o] 1.64236 :[font = text; inactive; preserveAspect; ] We bring in our Lorenz package: :[font = input; preserveAspect; ] <{"Position in Tunnel","Portal Image"}] :[font = postscript; PostScript; formatAsPostScript; output; inactive; preserveAspect; pictureLeft = 35; pictureWidth = 388; pictureHeight = 240; ] %! %%Creator: Mathematica %%AspectRatio: 0.61803 MathPictureStart % Scaling calculations 0.02381 0.09524 -0.10775 4.99022 [ [(2)] 0.21429 0.37877 0 1 Msboxa [(4)] 0.40476 0.37877 0 1 Msboxa [(6)] 0.59524 0.37877 0 1 Msboxa [(8)] 0.78571 0.37877 0 1 Msboxa [(10)] 0.97619 0.37877 0 1 Msboxa [(Position in Tunnel)] 1.00625 0.39127 -1 0 Msboxa [(0.04)] 0.01131 0.09186 1 0 Msboxa [(0.06)] 0.01131 0.19166 1 0 Msboxa [(0.08)] 0.01131 0.29147 1 0 Msboxa [(0.12)] 0.01131 0.49108 1 0 Msboxa [(0.14)] 0.01131 0.59088 1 0 Msboxa [(Portal Image)] 0.02381 0.62428 0 -1 Msboxa [ -0.001 -0.001 0 0 ] [ 1.001 0.61903 0 0 ] ] MathScale % Start of Graphics 1 setlinecap 1 setlinejoin newpath %%Object: Graphics [ ] 0 setdash 0 setgray gsave gsave 0.002 setlinewidth 0 0.39127 moveto 1 0.39127 lineto stroke 0.21429 0.38502 moveto 0.21429 0.39752 lineto stroke 0 setgray [(2)] 0.21429 0.37877 0 1 Mshowa 0.40476 0.38502 moveto 0.40476 0.39752 lineto stroke 0 setgray [(4)] 0.40476 0.37877 0 1 Mshowa 0.59524 0.38502 moveto 0.59524 0.39752 lineto stroke 0 setgray [(6)] 0.59524 0.37877 0 1 Mshowa 0.78571 0.38502 moveto 0.78571 0.39752 lineto stroke 0 setgray [(8)] 0.78571 0.37877 0 1 Mshowa 0.97619 0.38502 moveto 0.97619 0.39752 lineto stroke 0 setgray [(10)] 0.97619 0.37877 0 1 Mshowa 0 setgray [(Position in Tunnel)] 1.00625 0.39127 -1 0 Mshowa 0.02381 0 moveto 0.02381 0.61803 lineto stroke 0.01756 0.09186 moveto 0.03006 0.09186 lineto stroke 0 setgray [(0.04)] 0.01131 0.09186 1 0 Mshowa 0.01756 0.19166 moveto 0.03006 0.19166 lineto stroke 0 setgray [(0.06)] 0.01131 0.19166 1 0 Mshowa 0.01756 0.29147 moveto 0.03006 0.29147 lineto stroke 0 setgray [(0.08)] 0.01131 0.29147 1 0 Mshowa 0.01756 0.49108 moveto 0.03006 0.49108 lineto stroke 0 setgray [(0.12)] 0.01131 0.49108 1 0 Mshowa 0.01756 0.59088 moveto 0.03006 0.59088 lineto stroke 0 setgray [(0.14)] 0.01131 0.59088 1 0 Mshowa 0 setgray [(Portal Image)] 0.02381 0.62428 0 -1 Mshowa grestore grestore 0 0 moveto 1 0 lineto 1 0.618034 lineto 0 0.618034 lineto closepath clip newpath 0 setgray gsave gsave 0.004 setlinewidth 0.02381 0.39127 moveto 0.02381 0.38955 lineto 0.02381 0.38783 lineto 0.02382 0.38612 lineto 0.02382 0.38442 lineto 0.02384 0.38103 lineto 0.02387 0.37767 lineto 0.0239 0.37434 lineto 0.02394 0.37103 lineto 0.02405 0.3645 lineto 0.02418 0.35807 lineto 0.02434 0.35174 lineto 0.02476 0.33939 lineto 0.0253 0.32743 lineto 0.02595 0.31585 lineto 0.02763 0.29376 lineto 0.02979 0.27302 lineto 0.03245 0.25355 lineto 0.03928 0.21809 lineto 0.04347 0.20196 lineto 0.0482 0.1868 lineto 0.05932 0.15919 lineto 0.07277 0.13483 lineto 0.08873 0.11336 lineto 0.10738 0.09448 lineto 0.12896 0.07794 lineto 0.15371 0.06351 lineto 0.18196 0.05104 lineto 0.21403 0.0404 lineto 0.25032 0.0315 lineto 0.27018 0.02771 lineto 0.29127 0.02435 lineto 0.31365 0.02144 lineto 0.33739 0.019 lineto 0.34979 0.01797 lineto 0.36255 0.01706 lineto 0.37569 0.0163 lineto 0.38922 0.01567 lineto 0.39613 0.01541 lineto 0.40315 0.01519 lineto 0.41026 0.01501 lineto 0.41748 0.01487 lineto 0.42113 0.01482 lineto 0.4248 0.01478 lineto 0.4285 0.01474 lineto 0.43036 0.01473 lineto 0.43223 0.01472 lineto 0.4341 0.01472 lineto 0.43598 0.01472 lineto 0.43787 0.01472 lineto Mistroke 0.43976 0.01472 lineto 0.44167 0.01472 lineto 0.44357 0.01473 lineto 0.44549 0.01475 lineto 0.44741 0.01476 lineto 0.45127 0.0148 lineto 0.45516 0.01485 lineto 0.46303 0.015 lineto 0.47101 0.0152 lineto 0.4791 0.01545 lineto 0.49564 0.01615 lineto 0.51266 0.01712 lineto 0.53016 0.01839 lineto 0.54817 0.02 lineto 0.58576 0.02447 lineto 0.62553 0.0311 lineto 0.66761 0.04082 lineto 0.71212 0.05524 lineto 0.73533 0.06506 lineto 0.7592 0.07737 lineto 0.78374 0.09304 lineto 0.80899 0.11342 lineto 0.83495 0.14061 lineto 0.86164 0.17799 lineto 0.87527 0.20215 lineto 0.88909 0.23124 lineto 0.91732 0.30975 lineto 0.93173 0.36283 lineto 0.94635 0.42802 lineto 0.97619 0.60332 lineto Mfstroke grestore grestore % End of Graphics MathPictureEnd :[font = output; output; inactive; preserveAspect; endGroup; ] The Unformatted text for this cell was not generated. Use options in the Actions Settings dialog box to control when Unformatted text is generated. ;[o] -Graphics- ^*)