Changes in src/sas/sasgui/perspectives/fitting/media/mag_help.rst [eca66a1:5ed76f8] in sasview
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src/sas/sasgui/perspectives/fitting/media/mag_help.rst
reca66a1 r5ed76f8 4 4 .. by S King, ISIS, during SasView CodeCamp-III in Feb 2015. 5 5 6 .. |inlineimage004| image:: sm_image004. gif7 .. |inlineimage005| image:: sm_image005. gif8 .. |inlineimage008| image:: sm_image008. gif9 .. |inlineimage009| image:: sm_image009. gif10 .. |inlineimage010| image:: sm_image010. gif11 .. |inlineimage011| image:: sm_image011. gif12 .. |inlineimage012| image:: sm_image012. gif13 .. |inlineimage018| image:: sm_image018. gif14 .. |inlineimage019| image:: sm_image019. gif6 .. |inlineimage004| image:: sm_image004.png 7 .. |inlineimage005| image:: sm_image005.png 8 .. |inlineimage008| image:: sm_image008.png 9 .. |inlineimage009| image:: sm_image009.png 10 .. |inlineimage010| image:: sm_image010.png 11 .. |inlineimage011| image:: sm_image011.png 12 .. |inlineimage012| image:: sm_image012.png 13 .. |inlineimage018| image:: sm_image018.png 14 .. |inlineimage019| image:: sm_image019.png 15 15 16 16 … … 20 20 -------------------------------- 21 21 22 Magnetic scattering is implemented in five (2D) models 22 Magnetic scattering is implemented in five (2D) models 23 23 24 24 * *sphere* … … 28 28 * *parallelepiped* 29 29 30 In general, the scattering length density (SLD, = |beta|) in each region where the30 In general, the scattering length density (SLD, = $\beta$) in each region where the 31 31 SLD is uniform, is a combination of the nuclear and magnetic SLDs and, for polarised 32 32 neutrons, also depends on the spin states of the neutrons. 33 33 34 For magnetic scattering, only the magnetization component, *M*\ :sub:`perp`,35 perpendicular to the scattering vector *Q*contributes to the the magnetic34 For magnetic scattering, only the magnetization component, $M_\perp$, 35 perpendicular to the scattering vector $Q$ contributes to the the magnetic 36 36 scattering length. 37 37 38 .. image:: mag_vector. bmp38 .. image:: mag_vector.png 39 39 40 40 The magnetic scattering length density is then 41 41 42 .. image:: dm_eq. gif42 .. image:: dm_eq.png 43 43 44 where |gamma| = -1.913 is the gyromagnetic ratio, |mu|\ :sub:`B`is the45 Bohr magneton, *r*\ :sub:`0` is the classical radius of electron, and |sigma|44 where $\gamma = -1.913$ is the gyromagnetic ratio, $\mu_B$ is the 45 Bohr magneton, $r_0$ is the classical radius of electron, and $\sigma$ 46 46 is the Pauli spin. 47 47 … … 53 53 Spin-flips (+ -) and (- +) 54 54 55 .. image:: M_angles_pic. bmp55 .. image:: M_angles_pic.png 56 56 57 If the angles of the *Q* vector and the spin-axis (*x'*) to the *x*-axis are |phi|58 and |theta|\ :sub:`up`, respectively, then, depending on the spin state of the57 If the angles of the $Q$ vector and the spin-axis (*x'*) to the *x*-axis are $\phi$ 58 and $\theta_\text{up}$, respectively, then, depending on the spin state of the 59 59 neutrons, the scattering length densities, including the nuclear scattering 60 length density ( |beta|\ :sub:`N`) are60 length density ($\beta_N$) are 61 61 62 .. image:: sld1. gif62 .. image:: sld1.png 63 63 64 64 when there are no spin-flips, and 65 65 66 .. image:: sld2. gif66 .. image:: sld2.png 67 67 68 68 when there are, and 69 69 70 .. image:: mxp. gif70 .. image:: mxp.png 71 71 72 .. image:: myp. gif72 .. image:: myp.png 73 73 74 .. image:: mzp. gif74 .. image:: mzp.png 75 75 76 .. image:: mqx. gif76 .. image:: mqx.png 77 77 78 .. image:: mqy. gif78 .. image:: mqy.png 79 79 80 Here, *M*\ :sub:`0x`, *M*\ :sub:`0y` and *M*\ :sub:`0z` are the x, y and zcomponents81 of the magnetization vector given in the laboratory xyzframe given by80 Here, $M_{0x}$, $M_{0y}$ and $M_{0z}$ are the $x$, $y$ and $z$ components 81 of the magnetization vector given in the laboratory $xyz$ frame given by 82 82 83 .. image:: m0x_eq. gif83 .. image:: m0x_eq.png 84 84 85 .. image:: m0y_eq. gif85 .. image:: m0y_eq.png 86 86 87 .. image:: m0z_eq. gif87 .. image:: m0z_eq.png 88 88 89 and the magnetization angles |theta|\ :sub:`M` and |phi|\ :sub:`M`are defined in89 and the magnetization angles $\theta_M$ and $\phi_M$ are defined in 90 90 the figure above. 91 91 … … 93 93 94 94 =========== ================================================================ 95 M0_sld = *D*\ :sub:`M` *M*\ :sub:`0`96 Up_theta = |theta|\ :sub:`up`97 M_theta = |theta|\ :sub:`M`98 M_phi = |phi|\ :sub:`M`95 M0_sld = $D_M M_0$ 96 Up_theta = $\theta_\text{up}$ 97 M_theta = $\theta_M$ 98 M_phi = $\phi_M$ 99 99 Up_frac_i = (spin up)/(spin up + spin down) neutrons *before* the sample 100 100 Up_frac_f = (spin up)/(spin up + spin down) neutrons *after* the sample
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