Update explanation for RL problem

tutorial.ipynb

@@ -99,7 +99,7 @@
     "Alternatively, you can create the virtual env with\n",
     "\n",
     "```bash\n",
-    "python3 -m venv -n rl-tutorial\n",
+    "python3 -m venv rl-tutorial\n",
     "```\n",
     "\n",
     "and activate the env with `$ source <venv>/bin/activate` (bash) or `C:> <venv>/Scripts/activate.bat` (Windows)\n",
@@ -134,9 +134,9 @@
     }
    },
    "source": [
-    "<h2 style=\"color: #b51f2a\"> AWAKE (The Advanced Proton Driven Plasma Wakefield Acceleration Experiment)</h2>\n",
+    "<h2 style=\"color: #b51f2a\"> AWAKE Accelerator</h2>\n",
     "\n",
-    "AWAKE is an accelerator R&D project based at CERN. It investigates the use of plasma wakefields driven by a proton bunch to accelerate charged particles.\n",
+    "AWAKE (The Advanced Proton Driven Plasma Wakefield Acceleration Experiment) is an accelerator R&D project based at CERN. It investigates the use of plasma wakefields driven by a proton bunch to accelerate charged particles.\n",
     "- The proton beam from the SPS is used to drive wakefields in a plasma cell.\n",
     "- The wakefields in the plasma accelerate electrons coming from another beamline, like a surfer is accelerated by ocean waves.\n",
     "- Plasmas can support extremely strong electric fields, with accelerating gradients of GV/m over meter-scale distances, which can reduce the size of future accelerators."
@@ -150,12 +150,14 @@
     }
    },
    "source": [
-    "<h2 style=\"color: #b51f2a\"> AWAKE (The Advanced Proton Driven Plasma Wakefield Acceleration Experiment)</h2>\n",
+    "<h2 style=\"color: #b51f2a\"> AWAKE Accelerator</h2>\n",
     "<p>\n",
     "\n",
+    "(The Advanced Proton Driven Plasma Wakefield Acceleration Experiment)\n",
+    "\n",
     "</p>\n",
     "\n",
-    "<img src=\"img/awake.png\" style=\"width:40%; margin:auto;\"/>\n",
+    "<img src=\"img/awake.png\" style=\"width:60%; margin:auto;\"/>\n",
     "\n",
     "- **Momentum**: 10-20 MeV/c\n",
     "- **Electrons per bunch**: 1.2e9\n",
@@ -198,14 +200,21 @@
     "The problem is formulated in an episodic manner.\n",
     "\n",
     "<h3 style=\"color: #b51f2a\">Actions</h3>\n",
-    "The actions are the strenghts of 10 corrector magnets that can steer the beam.\n",
-    "They are normalized to [-1, 1], corresponding to $\\pm$ 100 mm.\n",
+    "The actuators are the strengths of 10 corrector magnets that can steer the beam.\n",
+    "They are normalized to [-1, 1]. \n",
+    "In this tutorial, we apply the action by adding a delta change $\\Delta a$ to the current magnet strengths .\n",
     "\n",
     "<h3 style=\"color: #b51f2a\">States/Observations</h3>\n",
-    "The observations are the readings of ten beam position monitors (BPMs), which read the position of the beam at a particular point in the beamline.\n",
+    "The observations are the readings of ten beam position monitors (BPMs), which read the position of the beam at a particular point in the beamline. The states are also normalized to [-1,1], corresponding to $\\pm$ 100 mm in the real accelerator.\n",
     "\n",
     "<h3 style=\"color: #b51f2a\">Reward</h3>\n",
-    "The reward is the negative RMS value of the distance to the target trajectory. "
+    "The reward is the negative RMS value of the distance to the target trajectory. \n",
+    "\n",
+    "$$\n",
+    "r(\\bm{O}) = - \\sqrt{ \\frac{1}{10} \\sum_{i=1}^{10} (O_{i} - O^{\\text{target}}_{i})^2},\n",
+    "$$\n",
+    "\n",
+    "where $\\bm{O}^{\\text{target}}=\\vec{0}$ for a centered orbit.\n"
    ]
   },
   {