(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 6.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 31575, 956] NotebookOptionsPosition[ 28914, 871] NotebookOutlinePosition[ 29780, 900] CellTagsIndexPosition[ 29737, 897] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell["Numerical answers, midterm exam 2009", "Subtitle", CellChangeTimes->{ 3.433174197289283*^9, 3.465809807806321*^9, {3.465809869195531*^9, 3.465809872562241*^9}}], Cell[CellGroupData[{ Cell["Constants and SI derived quantities :", "Subsubsection", CellChangeTimes->{3.442056239069137*^9}], Cell[BoxData[ RowBox[{ RowBox[{"(*", " ", RowBox[{ "Function", " ", "\"\\"", " ", "computes", " ", "and", " ", "displays", " ", "numerical", " ", "results"}], " ", "*)"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"SetAttributes", "[", RowBox[{"eq", ",", "HoldFirst"}], "]"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{ RowBox[{"eq", "[", RowBox[{"x_", ",", "y_"}], "]"}], ":=", RowBox[{"Block", "[", RowBox[{ RowBox[{"{", RowBox[{"s", "=", RowBox[{ RowBox[{"ToString", "[", RowBox[{"Unevaluated", "[", "x", "]"}], "]"}], "<>", " ", "\"\< =\>\""}]}], "}"}], ",", "\[IndentingNewLine]", RowBox[{ RowBox[{"x", "=", "y"}], ";", RowBox[{"Grid", "[", RowBox[{"{", RowBox[{"{", RowBox[{"s", ",", RowBox[{"ScientificForm", "[", RowBox[{ RowBox[{"N", "[", "x", "]"}], ",", "4"}], "]"}]}], "}"}], "}"}], "]"}]}]}], "]"}]}], ";"}]}]}]], "Input", CellChangeTimes->{{3.442053379509019*^9, 3.442053396504135*^9}, { 3.442053597630171*^9, 3.442053683312203*^9}, {3.442053830837649*^9, 3.442053901877917*^9}, {3.442054472098692*^9, 3.442054489349103*^9}, { 3.442054536108562*^9, 3.442054537969508*^9}, {3.442054592378005*^9, 3.442054601925389*^9}, {3.442054659668387*^9, 3.442054718800782*^9}, { 3.44205476417442*^9, 3.442054795683937*^9}, {3.442054839987955*^9, 3.442054843589749*^9}, 3.442055058001352*^9, {3.467729947011438*^9, 3.467729973563665*^9}, 3.467730613010619*^9}], Cell["\<\ mE = dipole moment of the Earth me = electron mass [kg]; mp = proton mass [kg]; ee = electron charge [C] p = ee(n0+ne+ni)kT, total pressure [Pa] ne = electron density [particles / m^3] te= temperature [K];\ \>", "Text", CellChangeTimes->{{3.442054253686097*^9, 3.442054265749793*^9}, { 3.442054341113421*^9, 3.442054347228541*^9}, {3.442055097104152*^9, 3.442055103627188*^9}, {3.442056075402776*^9, 3.442056087154217*^9}, 3.442056226606825*^9, {3.46773057924429*^9, 3.467730583771678*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"mE", "=", RowBox[{"8.8", " ", SuperscriptBox["10", "17"]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"me", "=", RowBox[{"9.1094", " ", SuperscriptBox["10", RowBox[{"-", "31"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"mp", "=", RowBox[{"1.6726", " ", SuperscriptBox["10", RowBox[{"-", "27"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ee", "=", RowBox[{"1.6022", " ", SuperscriptBox["10", RowBox[{"-", "19"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Epsilon]", "=", RowBox[{"8.8542", " ", SuperscriptBox["10", RowBox[{"-", "12"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Mu]0", "=", RowBox[{"4", "\[Pi]", " ", "\[Times]", SuperscriptBox["10", RowBox[{"-", "7"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"kB", "=", RowBox[{"1.3807", " ", SuperscriptBox["10", RowBox[{"-", "23"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"gE", "=", "9.8"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"rE", "=", RowBox[{"6.5", " ", SuperscriptBox["10", "6"]}]}], ";"}]}], "Input", CellChangeTimes->{{3.442043158626867*^9, 3.442043231321502*^9}, { 3.442043502031211*^9, 3.442043507013836*^9}, {3.442054299637162*^9, 3.442054300866091*^9}, 3.442056060025534*^9, {3.467730488737521*^9, 3.467730494070038*^9}, {3.467730527820964*^9, 3.467730564661491*^9}}] }, Open ]], Cell["Question 1", "Subsubsection", CellChangeTimes->{{3.442043343741751*^9, 3.442043345896352*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"eq", "[", RowBox[{"b", ",", RowBox[{"mE", "/", SuperscriptBox[ RowBox[{"(", RowBox[{"3", " ", "rE"}], ")"}], "3"]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"g", ",", RowBox[{"gE", "/", "9"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"vge", ",", RowBox[{"me", " ", RowBox[{ RowBox[{"g", "/", "ee"}], "/", "b"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"vgp", ",", RowBox[{"mp", " ", RowBox[{ RowBox[{"g", "/", "ee"}], "/", "b"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.44074706911927*^9, 3.440747124949056*^9}, { 3.442043367263417*^9, 3.442043467198015*^9}, {3.442044133680709*^9, 3.442044147501369*^9}, {3.442044194817998*^9, 3.442044241902228*^9}, { 3.442054362828731*^9, 3.44205441921861*^9}, {3.442054855068834*^9, 3.442054905628393*^9}, {3.467465799751321*^9, 3.467465821438238*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"b =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"1.187\"\>", "\[Times]", SuperscriptBox["10", "\<\"-4\"\>"]}], 0.00011868035536674591`, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442054912782724*^9, 3.442056279109236*^9, 3.467465965530808*^9, 3.467530852864259*^9, 3.467531390017725*^9, 3.467533038514438*^9, 3.467730464842689*^9, {3.467736831836929*^9, 3.467736844159286*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"g =\"\>", TagBox[ InterpretationBox["\<\"1.089\"\>", 1.088888888888889, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442054912782724*^9, 3.442056279109236*^9, 3.467465965530808*^9, 3.467530852864259*^9, 3.467531390017725*^9, 3.467533038514438*^9, 3.467730464842689*^9, {3.467736831836929*^9, 3.467736844172226*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"vge =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"5.216\"\>", "\[Times]", SuperscriptBox["10", "\<\"-8\"\>"]}], 5.216482724393165*^-8, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442054912782724*^9, 3.442056279109236*^9, 3.467465965530808*^9, 3.467530852864259*^9, 3.467531390017725*^9, 3.467533038514438*^9, 3.467730464842689*^9, {3.467736831836929*^9, 3.46773684417898*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"vgp =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"9.578\"\>", "\[Times]", SuperscriptBox["10", "\<\"-5\"\>"]}], 0.00009578116017322773, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442054912782724*^9, 3.442056279109236*^9, 3.467465965530808*^9, 3.467530852864259*^9, 3.467531390017725*^9, 3.467533038514438*^9, 3.467730464842689*^9, {3.467736831836929*^9, 3.467736844185613*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"eq", "[", RowBox[{"\[Omega]e", ",", RowBox[{"ee", " ", RowBox[{"b", "/", "me"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"\[Omega]i", ",", RowBox[{"ee", " ", RowBox[{"b", "/", "mp"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.442043575234716*^9, 3.442043575587754*^9}, { 3.442054925720272*^9, 3.442054940969481*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\[Omega]e =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"2.087\"\>", "\[Times]", SuperscriptBox["10", "\<\"7\"\>"]}], 2.0874005463433407`*^7, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442043581182382*^9, 3.44205494145503*^9, 3.442056279735202*^9, 3.467465965559127*^9, 3.467530853119647*^9, 3.467531390049695*^9, 3.467533038543032*^9, 3.467730464913734*^9, {3.467736831916744*^9, 3.467736844201965*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\[Omega]i =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"1.137\"\>", "\[Times]", SuperscriptBox["10", "\<\"4\"\>"]}], 11368.5080335167, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442043581182382*^9, 3.44205494145503*^9, 3.442056279735202*^9, 3.467465965559127*^9, 3.467530853119647*^9, 3.467531390049695*^9, 3.467533038543032*^9, 3.467730464913734*^9, {3.467736831916744*^9, 3.467736844208565*^9}}] }, Open ]], Cell["\<\ Gyroradii based on the thermal velocity and on the average velocity are both accepted.\ \>", "Text", CellChangeTimes->{{3.467730025637327*^9, 3.467730069221649*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"en", "=", "ee"}], ";"}], "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"eq", "[", RowBox[{"\[Rho]p1", ",", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", " ", RowBox[{"en", " ", "mp"}], "]"}], "/", "ee"}], "/", "b"}]}], "]"}], ",", RowBox[{"eq", "[", RowBox[{"\[Rho]p2", ",", RowBox[{ RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"2", " ", "en", " ", "mp"}], "]"}], "/", "ee"}], "/", "b"}]}], "]"}]}], "}"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"vgradB", ",", RowBox[{ RowBox[{ RowBox[{"en", "/", "ee"}], "/", "b"}], "/", RowBox[{"(", "rE", ")"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.442043632478175*^9, 3.442043691961148*^9}, { 3.442043793535394*^9, 3.442043816791393*^9}, {3.44205495338251*^9, 3.442054982314667*^9}, {3.467465918476638*^9, 3.467465956187934*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[GridBox[{ {"\<\"\[Rho]p1 =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"8.609\"\>", "\[Times]", SuperscriptBox["10", "\<\"-1\"\>"]}], 0.8609121647271191, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], ",", TagBox[GridBox[{ {"\<\"\[Rho]p2 =\"\>", TagBox[ InterpretationBox["\<\"1.218\"\>", 1.2175136593690719`, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]}], "}"}]], "Output", CellChangeTimes->{{3.442043681587205*^9, 3.442043695127779*^9}, 3.442043817924181*^9, 3.44205498327056*^9, 3.442056280016671*^9, 3.467465965652215*^9, 3.467530853289909*^9, 3.467531390071644*^9, 3.46753303856186*^9, 3.467730464936435*^9, {3.46773683193868*^9, 3.467736844225473*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"vgradB =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"1.296\"\>", "\[Times]", SuperscriptBox["10", "\<\"-3\"\>"]}], 0.0012963068181818182`, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{{3.442043681587205*^9, 3.442043695127779*^9}, 3.442043817924181*^9, 3.44205498327056*^9, 3.442056280016671*^9, 3.467465965652215*^9, 3.467530853289909*^9, 3.467531390071644*^9, 3.46753303856186*^9, 3.467730464936435*^9, {3.46773683193868*^9, 3.467736844232323*^9}}] }, Open ]], Cell["Question 2", "Subsubsection", CellChangeTimes->{{3.442043343741751*^9, 3.442043345896352*^9}, 3.442043850956666*^9}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"te", "=", "6000"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ne", "=", SuperscriptBox["10", "20"]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"eI", "=", RowBox[{"13.6", " ", "ee"}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"saha", "=", RowBox[{"2.4", " ", SuperscriptBox["10", RowBox[{"21", " "}]], " ", SuperscriptBox["te", RowBox[{"3", "/", "2"}]], RowBox[{"Exp", "[", RowBox[{ RowBox[{ RowBox[{"-", "eI"}], "/", "te"}], "/", "kB"}], "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"iondegree", ",", RowBox[{"saha", " ", "/", "ne"}]}], "]"}]}], "Input", CellChangeTimes->{{3.442044514472895*^9, 3.442044737017076*^9}, { 3.442054999797953*^9, 3.442055011475506*^9}, {3.46753083054931*^9, 3.467530830684854*^9}, 3.467531353392485*^9}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"iondegree =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"4.209\"\>", "\[Times]", SuperscriptBox["10", "\<\"-5\"\>"]}], 0.00004209168026567644, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442044668304234*^9, {3.442044717612468*^9, 3.442044737970746*^9}, 3.442055012137683*^9, 3.442056280297259*^9, 3.467465965751006*^9, 3.46753085346307*^9, 3.46753139009144*^9, 3.467533038583159*^9, 3.467730465002651*^9, {3.467736831998537*^9, 3.467736844364663*^9}}] }, Open ]], Cell["\<\ Debye lengths based on electron screening and on ion + electron screening are both accepted (formulas (8) and (15) of thelecture notes, respectively)\ \>", "Text", CellChangeTimes->{{3.467730103337889*^9, 3.467730167128381*^9}, { 3.467730213695805*^9, 3.467730233951432*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{"eq", "[", RowBox[{"\[Omega]p", ",", RowBox[{"ee", " ", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"ne", "/", "me"}], "/", "\[Epsilon]"}], "]"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"eq", "[", RowBox[{"\[Lambda]D1", ",", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"\[Epsilon]", " ", "te", " ", RowBox[{ RowBox[{"kB", "/", "2"}], "/", "ne"}]}], "]"}], "/", "ee"}]}], "]"}], ",", RowBox[{"eq", "[", RowBox[{"\[Lambda]D2", ",", RowBox[{ RowBox[{"Sqrt", "[", RowBox[{"\[Epsilon]", " ", "te", " ", RowBox[{"kB", "/", "ne"}]}], "]"}], "/", "ee"}]}], "]"}]}], "}"}], "\[IndentingNewLine]", RowBox[{"{", RowBox[{ RowBox[{"eq", "[", RowBox[{"nD1", ",", RowBox[{"ne", " ", RowBox[{"(", RowBox[{ RowBox[{"4", "/", "3"}], " ", "\[Pi]"}], ")"}], SuperscriptBox["\[Lambda]D1", "3"]}]}], "]"}], ",", RowBox[{"eq", "[", RowBox[{"nD2", ",", RowBox[{"ne", " ", RowBox[{"(", RowBox[{ RowBox[{"4", "/", "3"}], " ", "\[Pi]"}], ")"}], SuperscriptBox["\[Lambda]D2", "3"]}]}], "]"}]}], "}"}]}], "Input", CellChangeTimes->{{3.442048576286291*^9, 3.442048598928222*^9}, { 3.44204883806327*^9, 3.442048862002616*^9}, {3.44205502171769*^9, 3.442055043855098*^9}, {3.467465850078642*^9, 3.467465882327195*^9}, { 3.467466152761596*^9, 3.467466155279658*^9}, 3.467736826077899*^9}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\[Omega]p =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"5.642\"\>", "\[Times]", SuperscriptBox["10", "\<\"11\"\>"]}], 5.641533576218887*^11, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442048601501366*^9, 3.442048870640619*^9, 3.44205504442374*^9, 3.442056280754814*^9, 3.467465965888692*^9, 3.467466160232872*^9, 3.467530853604961*^9, 3.467531390108414*^9, 3.467533038659325*^9, 3.467730465055644*^9, {3.467736832010458*^9, 3.467736844467438*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[GridBox[{ {"\<\"\[Lambda]D1 =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"3.78\"\>", "\[Times]", SuperscriptBox["10", "\<\"-7\"\>"]}], 3.779794826152904*^-7, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], ",", TagBox[GridBox[{ {"\<\"\[Lambda]D2 =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"5.345\"\>", "\[Times]", SuperscriptBox["10", "\<\"-7\"\>"]}], 5.345437106133092*^-7, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]}], "}"}]], "Output", CellChangeTimes->{ 3.442048601501366*^9, 3.442048870640619*^9, 3.44205504442374*^9, 3.442056280754814*^9, 3.467465965888692*^9, 3.467466160232872*^9, 3.467530853604961*^9, 3.467531390108414*^9, 3.467533038659325*^9, 3.467730465055644*^9, {3.467736832010458*^9, 3.467736844472464*^9}}], Cell[BoxData[ RowBox[{"{", RowBox[{ TagBox[GridBox[{ {"\<\"nD1 =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"2.262\"\>", "\[Times]", SuperscriptBox["10", "\<\"1\"\>"]}], 22.6200358008748, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"], ",", TagBox[GridBox[{ {"\<\"nD2 =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"6.398\"\>", "\[Times]", SuperscriptBox["10", "\<\"1\"\>"]}], 63.97912282192419, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]}], "}"}]], "Output", CellChangeTimes->{ 3.442048601501366*^9, 3.442048870640619*^9, 3.44205504442374*^9, 3.442056280754814*^9, 3.467465965888692*^9, 3.467466160232872*^9, 3.467530853604961*^9, 3.467531390108414*^9, 3.467533038659325*^9, 3.467730465055644*^9, {3.467736832010458*^9, 3.467736844477725*^9}}] }, Open ]], Cell["Plug-in formulas (36) and (39) take temperatures in keV", "Text", CellChangeTimes->{{3.467730103337889*^9, 3.467730167128381*^9}, { 3.467730213695805*^9, 3.467730233951432*^9}, {3.467730285115942*^9, 3.467730304066551*^9}}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"tkeV", "=", RowBox[{"te", " ", RowBox[{ RowBox[{"kB", "/", "ee"}], "/", SuperscriptBox["10", "3"]}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Lambda]e", "=", RowBox[{"15.2", "-", RowBox[{"0.5", RowBox[{"Log", "[", RowBox[{"(", RowBox[{"ne", "/", SuperscriptBox["10", "20"]}], ")"}], "]"}]}], "+", RowBox[{"Log", "[", "tkeV", "]"}]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"\[Tau]e", ",", RowBox[{"1.09", " ", SuperscriptBox["10", "16"], RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", "tkeV", ")"}], RowBox[{"3", "/", "2"}]], "/", "ne"}], "/", "\[Lambda]e"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ve", "=", RowBox[{"Sqrt", "[", RowBox[{"te", " ", RowBox[{"kB", "/", "me"}]}], "]"}]}], ";"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"\[Lambda]mfp", ",", RowBox[{"ve", " ", "\[Tau]e"}]}], "]"}]}], "Input", CellChangeTimes->{ 3.400567360600228*^9, {3.400568643982437*^9, 3.40056866329508*^9}, { 3.433174319351582*^9, 3.433174359113074*^9}, {3.442048685924803*^9, 3.442048688961134*^9}, {3.442048739688547*^9, 3.442048812466369*^9}, { 3.442055156720665*^9, 3.442055176672353*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\[Tau]e =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"1.679\"\>", "\[Times]", SuperscriptBox["10", "\<\"-10\"\>"]}], 1.6790086912091715`*^-10, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442048813728667*^9, 3.442055179153592*^9, 3.442056281262018*^9, 3.467465966158984*^9, 3.467530853919357*^9, 3.467531390136793*^9, 3.467533038781999*^9, 3.467730465077801*^9, {3.467736832033858*^9, 3.467736844597709*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\[Lambda]mfp =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"5.063\"\>", "\[Times]", SuperscriptBox["10", "\<\"-5\"\>"]}], 0.00005063296332842438, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442048813728667*^9, 3.442055179153592*^9, 3.442056281262018*^9, 3.467465966158984*^9, 3.467530853919357*^9, 3.467531390136793*^9, 3.467533038781999*^9, 3.467730465077801*^9, {3.467736832033858*^9, 3.467736844603337*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"\[Omega]1", "=", SuperscriptBox["10", "9"]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Omega]2", "=", SuperscriptBox["10", "12"]}], ";"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"l2", ",", RowBox[{"2", RowBox[{"\[Pi]", "/", RowBox[{"Sqrt", "[", RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox["\[Omega]2", "2"], "-", SuperscriptBox["\[Omega]p", "2"]}], ")"}], "/", RowBox[{"(", RowBox[{"3", " ", "te", " ", RowBox[{"kB", "/", "me"}]}], ")"}]}], "]"}]}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.44204919914544*^9, 3.442049273416002*^9}, { 3.442049312901481*^9, 3.442049321990556*^9}, {3.442055187558269*^9, 3.442055208062008*^9}, {3.467533024063294*^9, 3.467533032412089*^9}, { 3.467730327585535*^9, 3.467730374340464*^9}, 3.467730424130473*^9, 3.467736813353509*^9}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"l2 =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"3.975\"\>", "\[Times]", SuperscriptBox["10", "\<\"-6\"\>"]}], 3.97479174357163*^-6, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.44204927607564*^9, 3.442049322878469*^9, 3.44205520863923*^9, 3.442056281810191*^9, 3.467465966359136*^9, 3.467530854175733*^9, 3.467531390232481*^9, 3.467533038885564*^9, 3.467730465094561*^9, { 3.467736818467033*^9, 3.467736844699442*^9}}] }, Open ]], Cell["Question 3", "Subsubsection", CellChangeTimes->{{3.442043343741751*^9, 3.442043345896352*^9}, 3.442043850956666*^9, 3.442049346381957*^9}], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"kt", "=", RowBox[{"5", " ", SuperscriptBox["10", "3"]}]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"ne", "=", SuperscriptBox["10", "20"]}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"b", "=", "5"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"\[Tau]e", "=", RowBox[{"7", " ", SuperscriptBox["10", RowBox[{"-", "5"}]]}]}], ";"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"\[Tau]ei", ",", RowBox[{ RowBox[{"(", RowBox[{"2", RowBox[{ RowBox[{"mp", "/", "2"}], "/", "me"}]}], ")"}], "\[Tau]e"}]}], "]"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"\[Eta]", ",", RowBox[{"me", "/", RowBox[{"(", RowBox[{"ne", " ", SuperscriptBox["ee", "2"], "\[Tau]e"}], ")"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.442049364920062*^9, 3.442049395479339*^9}, { 3.442049426739206*^9, 3.442049452284052*^9}, {3.44205521631598*^9, 3.442055222111494*^9}, {3.442055297266627*^9, 3.442055297549507*^9}, 3.46753083986113*^9, 3.467531375927593*^9}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\[Tau]ei =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"1.285\"\>", "\[Times]", SuperscriptBox["10", "\<\"-1\"\>"]}], 0.1285287724767822, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442049453325879*^9, 3.44205522282363*^9, 3.442055299992753*^9, 3.442056282136376*^9, 3.467465966536967*^9, 3.467530854325808*^9, 3.467531390252259*^9, 3.467533039122023*^9, 3.467730465257195*^9, { 3.467736832265983*^9, 3.467736844768074*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"\[Eta] =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"5.069\"\>", "\[Times]", SuperscriptBox["10", "\<\"-9\"\>"]}], 5.069420046214921*^-9, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442049453325879*^9, 3.44205522282363*^9, 3.442055299992753*^9, 3.442056282136376*^9, 3.467465966536967*^9, 3.467530854325808*^9, 3.467531390252259*^9, 3.467533039122023*^9, 3.467730465257195*^9, { 3.467736832265983*^9, 3.467736844802532*^9}}] }, Open ]], Cell[CellGroupData[{ Cell[BoxData[{ RowBox[{ RowBox[{"vloop", "=", "3"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"rmaj", "=", "6"}], ";"}], "\[IndentingNewLine]", RowBox[{ RowBox[{"rmin", "=", "2"}], ";"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"jtor", ",", RowBox[{"vloop", "/", RowBox[{"(", RowBox[{"2", "\[Pi]", " ", "rmaj", " ", "\[Eta]"}], ")"}]}]}], "]"}], "\[IndentingNewLine]", RowBox[{"eq", "[", RowBox[{"jdia", ",", RowBox[{"2", "ne", " ", "kt", " ", RowBox[{ RowBox[{"ee", "/", "rmin"}], "/", "b"}]}]}], "]"}]}], "Input", CellChangeTimes->{{3.442049575791408*^9, 3.442049611285654*^9}, { 3.442055237033668*^9, 3.442055272529223*^9}, {3.442065189277665*^9, 3.442065193616526*^9}, 3.467730636262139*^9}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"jtor =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"1.57\"\>", "\[Times]", SuperscriptBox["10", "\<\"7\"\>"]}], 1.569754938838894*^7, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442049612406939*^9, {3.442055249836745*^9, 3.442055275392097*^9}, 3.44205628248739*^9, 3.442065194545787*^9, 3.467465966786225*^9, 3.467530854470339*^9, 3.467531390273033*^9, 3.467533039299211*^9, 3.46773046539887*^9, 3.467730638944006*^9, {3.467736832359112*^9, 3.467736844920076*^9}}], Cell[BoxData[ TagBox[GridBox[{ {"\<\"jdia =\"\>", TagBox[ InterpretationBox[ RowBox[{"\<\"1.602\"\>", "\[Times]", SuperscriptBox["10", "\<\"4\"\>"]}], 16022.000000000002`, AutoDelete->True], ScientificForm[#, 4]& ]} }, AutoDelete->False, GridBoxItemSize->{"Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}], "Grid"]], "Output", CellChangeTimes->{ 3.442049612406939*^9, {3.442055249836745*^9, 3.442055275392097*^9}, 3.44205628248739*^9, 3.442065194545787*^9, 3.467465966786225*^9, 3.467530854470339*^9, 3.467531390273033*^9, 3.467533039299211*^9, 3.46773046539887*^9, 3.467730638944006*^9, {3.467736832359112*^9, 3.467736844949063*^9}}] }, Open ]] }, CellGrouping->Manual, WindowSize->{946, 971}, WindowMargins->{{131, Automatic}, {0, Automatic}}, PrintingCopies->1, PrintingPageRange->{Automatic, Automatic}, PageHeaders->{{Inherited, Inherited, Inherited}, {None, Inherited, None}}, PageHeaderLines->{Inherited, False}, PrintingOptions->{"Magnification"->1., "PaperOrientation"->"Portrait", "PaperSize"->{611.28, 789.57}, "PostScriptOutputFile"->"/home/emc/deblank/uu/examens/midterm/midtermexam2009_\ nb.pdf", "PrintCellBrackets"->False, "PrintMultipleHorizontalPages"->False, "PrintRegistrationMarks"->False, "PrintingMargins"->{{54, 54}, {72, 72}}}, FrontEndVersion->"7.0 for Linux x86 (32-bit) (February 25, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 173, 3, 62, "Subtitle"], Cell[CellGroupData[{ Cell[743, 27, 104, 1, 34, "Subsubsection"], Cell[850, 30, 1638, 40, 88, "Input"], Cell[2491, 72, 513, 12, 186, "Text"], Cell[3007, 86, 1510, 44, 232, "Input"] }, Open ]], Cell[4532, 133, 101, 1, 34, "Subsubsection"], Cell[CellGroupData[{ Cell[4658, 138, 957, 24, 89, "Input"], Cell[5618, 164, 627, 17, 36, "Output"], Cell[6248, 183, 546, 15, 32, "Output"], Cell[6797, 200, 626, 17, 36, "Output"], Cell[7426, 219, 628, 17, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[8091, 241, 392, 10, 50, "Input"], Cell[8486, 253, 658, 18, 36, "Output"], Cell[9147, 273, 652, 18, 36, "Output"] }, Open ]], Cell[9814, 294, 176, 4, 61, "Text"], Cell[CellGroupData[{ Cell[10015, 302, 930, 27, 69, "Input"], Cell[10948, 331, 1088, 31, 36, "Output"], Cell[12039, 364, 701, 18, 36, "Output"] }, Open ]], Cell[12755, 385, 127, 2, 34, "Subsubsection"], Cell[CellGroupData[{ Cell[12907, 391, 901, 26, 115, "Input"], Cell[13811, 419, 704, 18, 36, "Output"] }, Open ]], Cell[14530, 440, 288, 5, 61, "Text"], Cell[CellGroupData[{ Cell[14843, 449, 1522, 44, 75, "Input"], Cell[16368, 495, 702, 18, 36, "Output"], Cell[17073, 515, 1176, 33, 36, "Output"], Cell[18252, 550, 1150, 33, 36, "Output"] }, Open ]], Cell[19417, 586, 235, 3, 36, "Text"], Cell[CellGroupData[{ Cell[19677, 593, 1328, 38, 126, "Input"], Cell[21008, 633, 661, 18, 36, "Output"], Cell[21672, 653, 663, 18, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[22372, 676, 939, 24, 87, "Input"], Cell[23314, 702, 671, 18, 36, "Output"] }, Open ]], Cell[24000, 723, 149, 2, 34, "Subsubsection"], Cell[CellGroupData[{ Cell[24174, 729, 1107, 32, 146, "Input"], Cell[25284, 763, 676, 18, 36, "Output"], Cell[25963, 783, 677, 18, 36, "Output"] }, Open ]], Cell[CellGroupData[{ Cell[26677, 806, 773, 20, 107, "Input"], Cell[27453, 828, 721, 19, 36, "Output"], Cell[28177, 849, 721, 19, 36, "Output"] }, Open ]] } ] *) (* End of internal cache information *)