checked tutorials

Author: sergey-tomin

demos/ipython_tutorials/13_synchrotron_radiation_visualization.ipynb

@@ -257,7 +257,7 @@
      "output_type": "stream",
      "text": [
       "z = 93.40410100084 / 93.40410100084006 : applied: d:  \n",
-      " time exec: 7.94364595413208 sec\n"
+      " time exec: 8.964184761047363 sec\n"
      ]
     }
    ],
@@ -313,7 +313,7 @@
      "output_type": "stream",
      "text": [
       "z = 93.40410100084 / 93.40410100084006 : applied: d:  mTransform\n",
-      " time exec: 8.000734090805054 sec\n"
+      " time exec: 8.656868696212769 sec\n"
      ]
     },
     {

demos/ipython_tutorials/2_tracking.ipynb

@@ -213,7 +213,7 @@
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "z = 12.697400000000002 / 12.697400000000007 : applied: SpaceChargeetime exec:  65.20020890235901 sec\n"
+      "z = 12.697400000000002 / 12.697400000000007 : applied: SpaceChargeetime exec:  73.08316922187805 sec\n"
      ]
     }
    ],

demos/ipython_tutorials/3_space_charge.ipynb

@@ -362,7 +362,7 @@
      "text": [
       "tracking with Wakes .... \n",
       "z = 15.0 / 15.0 : applied: .0 : applied: Wake\n",
-      " time exec: 2.079639196395874 sec\n"
+      " time exec: 2.3191680908203125 sec\n"
      ]
     }
    ],

demos/ipython_tutorials/4_wake.ipynb

@@ -63,7 +63,7 @@
     "\\begin{equation}\n",
     "\\ddot{x} = \\frac{e}{\\gamma m_e} B_y \\dot{z}, \\qquad \\ddot{z} = -\\frac{e}{\\gamma m_e} B_y \\dot{x}\n",
     "\\end{equation}\n",
-    "\n",
+    "$$\\qquad$$\n",
     "In the first order approximation $v_z = \\dot{z} \\approx v = \\beta c = const$, $v_x << v_z$ and $\\ddot{z} \\approx 0$ and taking into account the undulator magnetic field $B_y = -B_0\\sin(k_y z)$ we get:\n",
     "\n",
     "\\begin{equation}\n",
@@ -76,9 +76,7 @@
     "x(z) = \\frac {K} {\\beta \\gamma k_u}\\sin(k_u z),\n",
     "\\end{equation}\n",
     "\n",
-    "where $K = \\frac{eB_0}{m_e c k_u}$\n",
-    "\n",
-    "and transverse velocity is \n",
+    "where $K = \\frac{eB_0}{m_e c k_u}$ and transverse velocity is \n",
     "\n",
     "\\begin{equation}\n",
     "v_x(t) = \\frac {K c}{\\gamma} \\cos(k_u \\beta c t) \\qquad or \\qquad v_x(z) = \\frac {K c}{\\gamma} \\cos(k_u z)\n",
@@ -97,7 +95,7 @@
     "\\begin{equation}\n",
     "v_z = \\sqrt{v^2 - v_x^2} = \\sqrt{c^2(1 - 1/\\gamma^2) - v_x^2} \\approx c\\left(1 - \\frac{1}{2\\gamma^2} (1 + \\gamma^2 v_x^2 / c^2) \\right)\n",
     "\\end{equation}\n",
-    "\n",
+    "$$\\quad$$\n",
     "Inserting for $v_x = \\dot{x}(t)$ and using the trigonometric identity $\\cos^2 \\alpha = (1 + \\cos 2 \\alpha)/2$\n",
     "\n",
     "\\begin{equation}\n",
@@ -136,7 +134,7 @@
     "E(x, y, z) = E_0 \\frac{ e^{-\\frac{1}{2} \\frac{x^2}{\\sigma_x^2 - j z/k} } } {\\sqrt{1-j z/(k \\sigma_x^2)}}\n",
     "\\frac{ e^{-\\frac{1}{2} \\frac{y^2}{\\sigma_y^2 - j z/k} } } {\\sqrt{1-j z/(k \\sigma_y^2)}}\n",
     "\\end{equation}\n",
-    "\n",
+    "$$\\quad$$\n",
     "Introducing [Rayleigh length](https://en.wikipedia.org/wiki/Rayleigh_length) for $x$ and $y$ plane:\n",
     "\n",
     "\\begin{equation}\n",
@@ -337,6 +335,7 @@
     "\\end{equation}\n",
     "\n",
     "<p>If we ensure fulfillment of the resonance condition only for the first harmonic as we did in the \"Option 1\" (in that case $n=0$) the only one term of the sum will survive  the only one term of the sum will survive. Indeed, for the $n=0$ argument of the exponential will be constant but for other harmonic numbers it will oscillate and give in average 0. So our final expression:</p>\n",
+    "\n",
     "\\begin{equation}\n",
     "\\boxed{\\Big \\langle  e^{j((k + k_u)\\overline v_z - \\omega) t} \\frac{e^{-j\\theta} + 1}{2} e^{-j Y \\sin\\theta}\\Big\\rangle = \\frac{J_{0}(Y) - J_1(Y)}{2}}\n",
     "\\end{equation}\n",
@@ -352,7 +351,7 @@
     "\\begin{equation}\n",
     "\\langle E v\\rangle = \\frac {K c}{\\gamma} Re  \\left\\{ E(x,y,z)\\right\\}\\frac{J_{0}(Y) - J_{1}(Y)}{2}\n",
     "\\end{equation}\n",
-    "\n",
+    "$$\\quad$$\n",
     "Finally, remembering derivation of the electric field amplitude $E_0 = \\sqrt{\\frac{4 Z_0 \\overline P(0) }{\\pi w^2}}$, we can write expression for amplitude of energy modulation on axis ($x=y=0$)\n",
     "\n",
     "\\begin{equation}\n",
@@ -618,9 +617,17 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 1,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "initializing ocelot...\n"
+     ]
+    }
+   ],
    "source": [
     "# the output of plotting commands is displayed inline within frontends, \n",
     "# directly below the code cell that produced it\n",
@@ -678,7 +685,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 2,
    "metadata": {},
    "outputs": [
     {
@@ -722,7 +729,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -744,7 +751,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -772,7 +779,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {},
    "outputs": [
     {