diff --git a/SS_deviation.nb b/SS_deviation.nb
deleted file mode 100644
index c4c712b4..00000000
--- a/SS_deviation.nb
+++ /dev/null
@@ -1,124 +0,0 @@
-(* Content-type: application/vnd.wolfram.mathematica *)
-
-(*** Wolfram Notebook File ***)
-(* http://www.wolfram.com/nb *)
-
-(* CreatedBy='Mathematica 11.2' *)
-
-(*CacheID: 234*)
-(* Internal cache information:
-NotebookFileLineBreakTest
-NotebookFileLineBreakTest
-NotebookDataPosition[       158,          7]
-NotebookDataLength[      3746,        114]
-NotebookOptionsPosition[      3098,         94]
-NotebookOutlinePosition[      3447,        109]
-CellTagsIndexPosition[      3404,        106]
-WindowFrame->Normal*)
-
-(* Beginning of Notebook Content *)
-Notebook[{
-
-Cell[CellGroupData[{
-Cell[BoxData[
- RowBox[{"Phi", " ", "=", " ", 
-  RowBox[{"\[Epsilon]", "*", 
-   RowBox[{"Cos", "[", 
-    RowBox[{
-     RowBox[{"\[Alpha]", "*", 
-      RowBox[{"Log", "[", 
-       RowBox[{"r", "/", "rs"}], "]"}]}], "-", " ", 
-     RowBox[{"m", "*", "\[Theta]"}]}], "]"}]}]}]], "Input",
- CellChangeTimes->{{3.812299324365906*^9, 3.812299356510524*^9}, {
-  3.812299402275013*^9, 3.8122995377713437`*^9}, {3.812299818940111*^9, 
-  3.8122998200058928`*^9}, {3.8122999006745744`*^9, 3.8122999093768873`*^9}, {
-  3.8123001559084597`*^9, 3.8123001721667376`*^9}, {3.812300299371953*^9, 
-  3.8123003015950623`*^9}},ExpressionUUID->"1a3cd121-f0d7-4b0b-8a31-\
-cef8810b9fb0"],
-
-Cell[BoxData[
- RowBox[{"\[Epsilon]", " ", 
-  RowBox[{"Cos", "[", 
-   RowBox[{
-    RowBox[{"m", " ", "\[Theta]"}], "-", 
-    RowBox[{"\[Alpha]", " ", 
-     RowBox[{"Log", "[", 
-      FractionBox["r", "rs"], "]"}]}]}], "]"}]}]], "Output",
- CellChangeTimes->{3.812299821517456*^9, 3.812299912268588*^9, 
-  3.812300302425089*^9},ExpressionUUID->"4bdcfee5-4a3f-47e2-8f72-\
-0eb84943074a"]
-}, Open  ]],
-
-Cell[CellGroupData[{
-
-Cell[BoxData[
- RowBox[{
-  RowBox[{"Simplify", "[", 
-   RowBox[{
-    RowBox[{"Laplacian", "[", 
-     RowBox[{"Phi", ",", 
-      RowBox[{"{", 
-       RowBox[{"r", ",", "\[Theta]", ",", "z"}], "}"}], ",", 
-      "\"\<Cylindrical\>\""}], "]"}], " ", "/", " ", 
-    RowBox[{"(", 
-     RowBox[{"4", "*", "\[Pi]", "*", "G"}], ")"}]}], "]"}], 
-  "\[IndentingNewLine]"}]], "Input",
- CellChangeTimes->{{3.8122998802940083`*^9, 3.8122998856883087`*^9}, {
-  3.8122999428034587`*^9, 3.8122999445556717`*^9}, {3.8122999842974052`*^9, 
-  3.8123001315872946`*^9}, {3.812300177352112*^9, 3.8123001803575807`*^9}, {
-  3.812300213842621*^9, 
-  3.812300395212168*^9}},ExpressionUUID->"d2abdc2c-8726-44cf-b72d-\
-1bcf85b987d6"],
-
-Cell[BoxData[
- RowBox[{"-", 
-  FractionBox[
-   RowBox[{
-    RowBox[{"(", 
-     RowBox[{
-      SuperscriptBox["m", "2"], "+", 
-      SuperscriptBox["\[Alpha]", "2"]}], ")"}], " ", "\[Epsilon]", " ", 
-    RowBox[{"Cos", "[", 
-     RowBox[{
-      RowBox[{"m", " ", "\[Theta]"}], "-", 
-      RowBox[{"\[Alpha]", " ", 
-       RowBox[{"Log", "[", 
-        FractionBox["r", "rs"], "]"}]}]}], "]"}]}], 
-   RowBox[{"4", " ", "G", " ", "\[Pi]", " ", 
-    SuperscriptBox["r", "2"]}]]}]], "Output",
- CellChangeTimes->{{3.812300115175284*^9, 3.812300134601759*^9}, {
-   3.81230026401114*^9, 3.8123003186143255`*^9}, 3.8123003504348726`*^9, 
-   3.812300396173873*^9},ExpressionUUID->"838887bb-5b71-45cf-87cd-\
-50eefe8b75b6"]
-}, Open  ]]
-},
-WindowSize->{759, 526},
-WindowMargins->{{Automatic, 108}, {101, Automatic}},
-FrontEndVersion->"11.2 for Microsoft Windows (64-bit) (September 10, 2017)",
-StyleDefinitions->"Default.nb"
-]
-(* End of Notebook Content *)
-
-(* Internal cache information *)
-(*CellTagsOutline
-CellTagsIndex->{}
-*)
-(*CellTagsIndex
-CellTagsIndex->{}
-*)
-(*NotebookFileOutline
-Notebook[{
-Cell[CellGroupData[{
-Cell[580, 22, 662, 14, 28, "Input",ExpressionUUID->"1a3cd121-f0d7-4b0b-8a31-cef8810b9fb0"],
-Cell[1245, 38, 382, 10, 53, "Output",ExpressionUUID->"4bdcfee5-4a3f-47e2-8f72-0eb84943074a"]
-}, Open  ]],
-Cell[CellGroupData[{
-Cell[1664, 53, 705, 17, 48, "Input",ExpressionUUID->"d2abdc2c-8726-44cf-b72d-1bcf85b987d6"],
-Cell[2372, 72, 710, 19, 103, "Output",ExpressionUUID->"838887bb-5b71-45cf-87cd-50eefe8b75b6"]
-}, Open  ]]
-}
-]
-*)
-
-(* End of internal cache information *)
-
diff --git a/notebooks/spiral_derivation.nb b/notebooks/spiral_derivation.nb
new file mode 100644
index 00000000..bb69390a
--- /dev/null
+++ b/notebooks/spiral_derivation.nb
@@ -0,0 +1,185 @@
+(* Content-type: application/vnd.wolfram.mathematica *)
+
+(*** Wolfram Notebook File ***)
+(* http://www.wolfram.com/nb *)
+
+(* CreatedBy='Mathematica 11.2' *)
+
+(*CacheID: 234*)
+(* Internal cache information:
+NotebookFileLineBreakTest
+NotebookFileLineBreakTest
+NotebookDataPosition[       158,          7]
+NotebookDataLength[      6735,        177]
+NotebookOptionsPosition[      5606,        150]
+NotebookOutlinePosition[      5942,        165]
+CellTagsIndexPosition[      5899,        162]
+WindowFrame->Normal*)
+
+(* Beginning of Notebook Content *)
+Notebook[{
+Cell[BoxData[
+ RowBox[{"ClearAll", "[", "\"\<Global`*\>\"", "]"}]], "Input",
+ CellChangeTimes->{{3.814898753475795*^9, 3.8148987534850597`*^9}},
+ CellLabel->"In[27]:=",ExpressionUUID->"86574956-c5fa-4fd0-8266-ec62114b08b6"],
+
+Cell[CellGroupData[{
+
+Cell["Spiral Feature Potential / Density Pair", "Section",
+ CellChangeTimes->{{3.814898411903373*^9, 3.814898439505828*^9}, {
+  3.814899148402547*^9, 
+  3.814899158132937*^9}},ExpressionUUID->"fbd0bc36-a86f-4130-b227-\
+90d4ae1639e0"],
+
+Cell[TextData[{
+ "Let:\n- ",
+ Cell[BoxData[
+  FormBox[
+   SubscriptBox["r", "s"], TraditionalForm]],
+  FormatType->"TraditionalForm",ExpressionUUID->
+  "0b5e7051-296a-4355-b655-2bfa459c62b4"],
+ " be the scale length\n- m the phase wrap"
+}], "Text",
+ CellChangeTimes->{{3.814898509820797*^9, 3.8148985447486687`*^9}, {
+  3.8148990866275787`*^9, 3.8148991021862793`*^9}, {3.8148991652215137`*^9, 
+  3.81489917052065*^9}},ExpressionUUID->"19a5019d-b896-4cb7-837b-\
+7887271f5a7f"],
+
+Cell["The Potential is given by:", "Text",
+ CellChangeTimes->{{3.814899187539977*^9, 3.8148991908563004`*^9}, {
+  3.814899369471631*^9, 
+  3.814899371445347*^9}},ExpressionUUID->"4c4c4f32-80b8-4585-89ba-\
+4b9fd4336000"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{" ", 
+  RowBox[{"Phi", "=", " ", 
+   RowBox[{"\[Epsilon]", "*", 
+    RowBox[{"Cos", "[", 
+     RowBox[{
+      RowBox[{"\[Alpha]", "*", 
+       RowBox[{"Log", "[", 
+        FractionBox["r", "rs"], "]"}]}], "-", " ", 
+      RowBox[{"m", "*", "\[Theta]"}]}], "]"}]}]}]}]], "Input",
+ CellChangeTimes->{{3.812299324365906*^9, 3.812299356510524*^9}, {
+  3.812299402275013*^9, 3.8122995377713437`*^9}, {3.812299818940111*^9, 
+  3.8122998200058928`*^9}, {3.8122999006745744`*^9, 3.8122999093768873`*^9}, {
+  3.8123001559084597`*^9, 3.8123001721667376`*^9}, {3.812300299371953*^9, 
+  3.8123003015950623`*^9}, {3.8148984544274282`*^9, 3.814898475035756*^9}, {
+  3.81489855484459*^9, 3.814898577155437*^9}, {3.814898633417138*^9, 
+  3.814898635249322*^9}, {3.814898763117502*^9, 3.8148987642580557`*^9}},
+ CellLabel->"In[28]:=",ExpressionUUID->"1a3cd121-f0d7-4b0b-8a31-cef8810b9fb0"],
+
+Cell[BoxData[
+ RowBox[{"\[Epsilon]", " ", 
+  RowBox[{"Cos", "[", 
+   RowBox[{
+    RowBox[{"m", " ", "\[Theta]"}], "-", 
+    RowBox[{"\[Alpha]", " ", 
+     RowBox[{"Log", "[", 
+      FractionBox["r", "rs"], "]"}]}]}], "]"}]}]], "Output",
+ CellChangeTimes->{
+  3.812299821517456*^9, 3.812299912268588*^9, 3.812300302425089*^9, {
+   3.814898580400764*^9, 3.8148985968367987`*^9}, 3.8148986390785227`*^9, 
+   3.814898691994795*^9, {3.814898757272633*^9, 3.814898764667898*^9}, 
+   3.814899303232542*^9, 3.8148993429027147`*^9},
+ CellLabel->"Out[28]=",ExpressionUUID->"1874f154-4561-41e9-8648-70286f4dd403"]
+}, Open  ]],
+
+Cell[TextData[{
+ "The density is given by solving Poisson\[CloseCurlyQuote]s equation:\n",
+ Cell[BoxData[
+  RowBox[{
+   RowBox[{
+    SuperscriptBox["\[Del]", "2"], "\[CapitalPhi]"}], "=", 
+   RowBox[{"4", "\[Pi]G", " ", "\[Rho]"}]}]], "Input",ExpressionUUID->
+  "43d21002-6ff2-466e-bc15-82ee854615a1"]
+}], "Text",
+ CellChangeTimes->{{3.814899187539977*^9, 
+  3.814899281005931*^9}},ExpressionUUID->"c0761ce3-c877-4b9c-9c81-\
+c6d5e2d25761"],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"rho", " ", "=", " ", 
+  RowBox[{"Simplify", "[", 
+   RowBox[{
+    FractionBox["1", 
+     RowBox[{"4", "*", "\[Pi]", "*", "G"}]], 
+    RowBox[{"Laplacian", "[", 
+     RowBox[{"Phi", ",", 
+      RowBox[{"{", 
+       RowBox[{"r", ",", "\[Theta]", ",", "z"}], "}"}], ",", 
+      "\"\<Cylindrical\>\""}], "]"}]}], "]"}]}]], "Input",
+ CellChangeTimes->{{3.8122998802940083`*^9, 3.8122998856883087`*^9}, {
+   3.8122999428034587`*^9, 3.8122999445556717`*^9}, {3.8122999842974052`*^9, 
+   3.8123001315872946`*^9}, {3.812300177352112*^9, 3.8123001803575807`*^9}, {
+   3.812300213842621*^9, 3.812300395212168*^9}, 3.814898587696806*^9, {
+   3.8148986378066597`*^9, 3.814898671700964*^9}, 3.814899298327828*^9, {
+   3.814899330040409*^9, 3.814899335804686*^9}},
+ CellLabel->"In[29]:=",ExpressionUUID->"d2abdc2c-8726-44cf-b72d-1bcf85b987d6"],
+
+Cell[BoxData[
+ RowBox[{"-", 
+  FractionBox[
+   RowBox[{
+    RowBox[{"(", 
+     RowBox[{
+      SuperscriptBox["m", "2"], "+", 
+      SuperscriptBox["\[Alpha]", "2"]}], ")"}], " ", "\[Epsilon]", " ", 
+    RowBox[{"Cos", "[", 
+     RowBox[{
+      RowBox[{"m", " ", "\[Theta]"}], "-", 
+      RowBox[{"\[Alpha]", " ", 
+       RowBox[{"Log", "[", 
+        FractionBox["r", "rs"], "]"}]}]}], "]"}]}], 
+   RowBox[{"4", " ", "G", " ", "\[Pi]", " ", 
+    SuperscriptBox["r", "2"]}]]}]], "Output",
+ CellChangeTimes->{{3.812300115175284*^9, 3.812300134601759*^9}, {
+   3.81230026401114*^9, 3.8123003186143255`*^9}, 3.8123003504348726`*^9, 
+   3.812300396173873*^9, {3.8148985908747063`*^9, 3.814898599334854*^9}, {
+   3.814898641012828*^9, 3.8148986465962973`*^9}, 3.81489869204513*^9, {
+   3.8148987572870483`*^9, 3.8148987668736563`*^9}, 3.814899303261135*^9, {
+   3.814899333710416*^9, 3.814899342924374*^9}},
+ CellLabel->"Out[29]=",ExpressionUUID->"6ffec622-7e08-4c74-80e0-624b54792097"]
+}, Open  ]]
+}, Open  ]]
+},
+WindowSize->{956, 769},
+WindowMargins->{{Automatic, 9}, {Automatic, 13}},
+FrontEndVersion->"12.0 for Mac OS X x86 (64-bit) (April 8, 2019)",
+StyleDefinitions->"Default.nb"
+]
+(* End of Notebook Content *)
+
+(* Internal cache information *)
+(*CellTagsOutline
+CellTagsIndex->{}
+*)
+(*CellTagsIndex
+CellTagsIndex->{}
+*)
+(*NotebookFileOutline
+Notebook[{
+Cell[558, 20, 223, 3, 30, "Input",ExpressionUUID->"86574956-c5fa-4fd0-8266-ec62114b08b6"],
+Cell[CellGroupData[{
+Cell[806, 27, 233, 4, 67, "Section",ExpressionUUID->"fbd0bc36-a86f-4130-b227-90d4ae1639e0"],
+Cell[1042, 33, 476, 12, 81, "Text",ExpressionUUID->"19a5019d-b896-4cb7-837b-7887271f5a7f"],
+Cell[1521, 47, 219, 4, 35, "Text",ExpressionUUID->"4c4c4f32-80b8-4585-89ba-4b9fd4336000"],
+Cell[CellGroupData[{
+Cell[1765, 55, 895, 17, 46, "Input",ExpressionUUID->"1a3cd121-f0d7-4b0b-8a31-cef8810b9fb0"],
+Cell[2663, 74, 602, 13, 49, "Output",ExpressionUUID->"1874f154-4561-41e9-8648-70286f4dd403"]
+}, Open  ]],
+Cell[3280, 90, 439, 11, 52, "Text",ExpressionUUID->"c0761ce3-c877-4b9c-9c81-c6d5e2d25761"],
+Cell[CellGroupData[{
+Cell[3744, 105, 852, 17, 48, "Input",ExpressionUUID->"d2abdc2c-8726-44cf-b72d-1bcf85b987d6"],
+Cell[4599, 124, 979, 22, 59, "Output",ExpressionUUID->"6ffec622-7e08-4c74-80e0-624b54792097"]
+}, Open  ]]
+}, Open  ]]
+}
+]
+*)
+