Symbols
|
Table 11.3: TABLE OF MATHEMATICAL SYMBOLS If no units are given, then quantity is dimensionless, or if the units are given as \(?\), then the dimensions depend on context. Generally, the usage of symbols tries to follow that from the Plasma Formulary ref. [18], in SI units, with temperatures specified as \(kT\) which returns \(J\). The Formulary also give the fundamental dimensions of the SI units, which should enable checking of dimensional consistency of equations, eg. magnetic field induction is in Tesla (\(T\)) whence the fundamental dimension expression gives \(T=kg s^{-1} C^{-1}\). Note that the symbols are sorted by font as well as alphabet, so that boldface symbols appear immediately after ‘b’ (backslashes ignored). The main source for the symbols is the Equations document ref. [110], also included are those listed as used in the text by Karniadakis and Sherwin ref. [111], prefaced by (K+S), plus symbols used in the report ref. [59]. |
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|
Symbol |
Description |
Units |
|
\(a\) |
minor radius of the torus (horizontal) |
\(m\) |
|
\(a_{ij}\) |
coefficient of matrix \(A\) |
|
|
\(A\) |
atomic mass of ion |
|
|
\(A_i\) |
atomic mass of ion |
|
|
\(A_\alpha \) |
atomic mass of ion species \(\alpha \) |
|
|
\([a,b]\) |
arbitrary finite interval |
|
|
\(\alpha \) |
as suffix is species label or index |
|
|
\(\alpha _n\) |
perturbation amplitude |
|
|
\(\alpha ^{Z_p\rightarrow Z}\) |
partial dielectronic recombination rate coefficient |
\(m^3 s^{-1}\) |
|
\(\alpha ^{Z\rightarrow Z_m}\) |
partial dielectronic recombination rate coefficient |
\(m^3 s^{-1}\) |
|
\(b\) |
minor radius of the torus (vertical) |
\(m\) |
|
\(B_0\) |
used to make \(B\) dimensionless |
\(T\) |
|
\(B_s\) |
characteristic magnetic field used to make \(\bf B\) dimensionless |
\(T\) |
|
\(\bar {N}_Z\) |
average number of charge states |
|
|
\(B=|{\bf B}|\) |
amplitude of the imposed magnetic field |
\(T\) |
|
\(B_T\) |
amplitude of the imposed toroidal magnetic field |
\(T\) |
|
\(\beta \) |
as suffix is species label |
|
|
\(\beta \) |
(Glossary) Ratio of plasma pressure to pressure in magnetic field |
|
|
\({\bf a} = d^2 {\bf x}/dt^2\) |
acceleration experienced by a particle |
\(m^2 s^{-1}\) |
|
\({\bf A}({\bf x},t)\) |
magnetic vector potential |
\(T m\) |
|
\({\bf B}({\bf x},t)\) |
magnetic field |
\(T\) |
|
\(\bf b\) |
unit vector giving the direction of the magnetic field |
|
|
\({\bf E}({\bf x},t)\) |
electric field |
\(V m^{-1}\) |
|
\(E_s\) |
characteristic electric field used to make \(\bf E\) dimensionless |
\(V m^{-1}\) |
|
\({\bf E}^{+}\) |
modified electric field |
\(m^{-2}\) |
|
\(\bf F\) |
force vector |
\(N\) |
|
\({\bf u}_\wedge \) |
pseudo / thermal velocity component in flux surface normal to field direction |
\(m s^{-1}\) |
|
\(\bf v\) |
generic velocity |
\(m s^{-1}\) |
|
\({\bf v}_\alpha \) |
velocity of species \(\alpha \) |
\(m s^{-1}\) |
|
\({\bf v}_{\|}\) |
fluid velocity directed along fieldline |
\(m s^{-1}\) |
|
\({\bf v}_\perp \) |
fluid velocity component normal to flux surface |
\(m s^{-1}\) |
|
\({\bf v}_\wedge \) |
fluid velocity component in flux surface normal to field direction |
\(m s^{-1}\) |
|
\({\bf v}_0\) |
initial fluid velocity |
\(m s^{-1}\) |
|
\({\bf v}_{cx}\) |
‘charge exchange’ perpendicular fluid velocity component |
\(m s^{-1}\) |
|
\({\bf v}_{E \times B}\) |
‘E cross B’ perpendicular fluid velocity component |
\(m s^{-1}\) |
|
\({\bf v}_e\) |
velocity of the electrons |
\(m s^{-1}\) |
|
\({\bf v}_i\) |
velocity of the ion species |
\(m s^{-1}\) |
|
\({\bf v}_{e \nabla B}\) |
‘grad B’ perpendicular fluid velocity component for electrons |
\(m s^{-1}\) |
|
\({\bf v}_{i \nabla B}\) |
‘grad B’ perpendicular fluid velocity component for ions |
\(m s^{-1}\) |
|
\({\bf v}_\textrm {diff}\) |
‘diffusive’ perpendicular fluid velocity component |
\(m s^{-1}\) |
|
\({\bf x}=\left (x_1,x_2,\dots ,x_d\right )\) |
is a \(d\)-dimensional vector |
|
|
\(\bf x\) |
position |
\(m\) |
|
\(b_n\) |
‘b-factors’ ref. [112, slide 21] |
|
|
\(\boldsymbol {\xi }(\theta )\) |
multi-dimensional random variable with a specific probability distribution as a function of the random parameter \(0\leq \theta \leq 1\) |
|
|
\(\boldsymbol {B}\) |
(K+S) Basis matrix |
|
|
\(\boldsymbol {D}_{\xi }\) |
(K+S) Elemental derivative matrix with respect to \(\xi \) |
|
|
\(\boldsymbol {f}^e\) |
(K+S) Force vector of the \(e\)th element |
|
|
\(\boldsymbol {H}\) |
(K+S) Helmholtz matrix (\(=\mathcal {A}^T \underline {\boldsymbol {H}^e} \mathcal {A}\))) |
|
|
\(\boldsymbol {H}^e\) |
(K+S) Elemental Helmholtz matrix |
|
|
\(\boldsymbol {L}\) |
(K+S) Laplacian matrix (\(=\mathcal {A}^T \underline {\boldsymbol {L}^e} \mathcal {A}\))) |
|
|
\(\boldsymbol {\Lambda }(u)\) |
(K+S) Diagonal matrix of \(u(\xi _i, \xi _2)\) evaluated at quadrature points |
|
|
\(\boldsymbol {L}^e\) |
(K+S) Elemental Laplacian matrix |
|
|
\(\boldsymbol {M}\) |
(K+S) Mass matrix (\(=\mathcal {A}^T \underline {\boldsymbol {M}^e} \mathcal {A}\)) |
|
|
\(\boldsymbol {\mathcal {A}}^T\) |
(K+S) Matrix global assembly |
|
|
\(\boldsymbol {M}^e\) |
(K+S) Elemental mass matrix |
|
|
\(\boldsymbol {n}\) |
(K+S) Unit outward normal |
|
|
\(\boldsymbol {\omega }\) |
(K+S and plasma models) Vorticity |
\(s^{-1}\) or \(C m^{-3}\) |
|
\(\boldsymbol {u}^e\) |
(K+S) Vector containing function evaluated at quadrature points |
|
|
\(\boldsymbol {W}\) |
(K+S) Diagonal weight / Jacobian matrix |
|
|
\(\boldsymbol {\xi }(\theta )\) |
multi-dimensional random variable with a specific probability distribution as a function of the random parameter \(0\leq \theta \leq 1\) |
|
|
\(B_p\) |
amplitude of the poloidal magnetic field |
\(T\) |
|
\(C_0=\sqrt {K_{MA} T_0}\) |
used to make velocities dimensionless |
\(m s^{-1}\) |
|
\(\cap \) |
(Sets) Set intersection |
|
|
\(\chi \) |
(K+S) Space of trial solutions |
|
|
\(\chi ^{\delta }\) |
(K+S) Finite-dimensional space of trial solutions |
|
|
\(\chi _i(\xi )\) |
(FE Basis) Local Cartesian to global coordinate mapping |
|
|
\(c_p\) |
specific heat at constant pressure |
\(J kg^{-1} K^{-1}\) |
|
\(c_s = \sqrt {\frac {kT_i + {Z_i} kT_e}{{m_i}}}\) |
approx. plasma acoustic speed |
\(m s^{-1}\) |
|
\(c_s = \sqrt {\frac {p}{\rho _m}}\) |
plasma acoustic speed |
\(m s^{-1}\) |
|
\(c_{se} = \sqrt {\frac {kT_e}{{m_e}}}\) |
acoustic speed of electrons |
\(m s^{-1}\) |
|
\(c_{si} = \sqrt {\frac {kT_i}{{m_i}}}\) |
acoustic speed of ions |
\(m s^{-1}\) |
|
\(C_S\) |
sound speed coefficient in radiation equation |
\(m s^{-1}\) |
|
\(\cup \) |
(Sets) Set union |
|
|
\(C(x_i, x_j)\) |
covariance of random variables \(x_i\), \(x_j\) |
|
|
\(d\) |
number of dimensions over which the integral is performed |
|
|
\(\delta p_i\) |
stress tensor |
\(N m^{-2}\) |
|
\(\delta \) |
Kronecker delta |
|
|
\(\delta _D\) |
Dirac delta function |
|
|
\(\delta _e\) |
energy flux factor at boundary of the electrons |
|
|
\(\delta =\frac {1}{2}(\delta _e+\delta _i)\) |
energy flux factor at boundary of ‘mean’ species |
|
|
\(\delta _i\) |
energy flux factor at boundary of the ion species |
|
|
\(\delta _\alpha \) |
(Glossary) Magnetisation parameter, species \(\alpha \) gyroradius normalised to \(L\) |
|
|
\(\delta (x)\) |
Dirac delta function of continuous real variable \(x\) |
|
|
\(D\) |
spatial dimensionality of problem |
|
|
\(D_A\) |
diffusion coefficient for plasma charges in a background of neutrals |
\(m^2 s^{-1}\) |
|
\(D_e\) |
diffusion coefficient for electrons, eg. in a background of neutrals |
\(m^2 s^{-1}\) |
|
\(D_{fv\alpha }\) |
scale dissipation in equation for evolution of species velocity \({\bf v}_\alpha \) |
|
|
\(D_n\) |
neutral diffusion coefficient |
\(m^2 s^{-1}\) |
|
\(D_{fp\alpha }\) |
scale dissipation in equation for evolution of species pressure/energy \(p_\alpha \) |
|
|
\(D_i\) |
diffusion coefficient for ions, eg. in a background of neutrals |
\(m^2 s^{-1}\) |
|
\(|e|\) |
absolute value of the charge on the electron |
\(C\) |
|
\(e\) |
(K+S) Finite element number \(1 \leq e \leq N_{el}\) |
|
|
\(e_{ijk}\) |
weighted integral of triple products of \(\Psi _i\) of the ion species |
|
|
\(\emptyset \) |
(Sets) Empty set |
|
|
\(\epsilon _0\) |
permittivity of free space |
\(F m^{-1}\) |
|
\(\epsilon _r=t_s/t_0\) |
scale factor for transient term |
|
|
\(\eta _1, \eta _2, \eta _3\) |
(FE Basis) Local collapsed Cartesian coordinates |
|
|
\(\eta _B\) |
plasma resistivity after Braginskii |
\(\Omega m\) |
|
\(\eta _d=\eta _B/\mu _0\) |
plasma resistivity, as diffusivity |
\(m^2 s^{-1}\) |
|
\(\eta _{e{\sf n}}\) |
contribution to plasma resistivity, as diffusivity, from electron-neutral interactions |
\(m^2 s^{-1}\) |
|
\(\eta _{e{\sf n}\|}\) |
contribution to plasma parallel resistivity, as diffusivity, from electron-neutral interactions |
\(m^2 s^{-1}\) |
|
\(\eta _{i{\sf n}}\) |
contribution to plasma resistivity, as diffusivity, from ion-neutral interactions |
\(m^2 s^{-1}\) |
|
\(\eta _{i{\sf n}\|}\) |
contribution to plasma parallel resistivity, as diffusivity, from ion-neutral interactions |
\(m^2 s^{-1}\) |
|
\(f_0\) |
constant in the expansion of \(f\left (x_1,\ldots ,x_d\right )\) |
|
|
\(f_0\) |
initial distribution function of the electrons |
\(m^{-6} s^3\) |
|
\(f_\alpha \) |
distribution function of species \(\alpha \) |
\(m^{-6} s^3\) |
|
\(f_e\) |
distribution function of the electrons |
\(m^{-6} s^3\) |
|
\(f_i\) |
distribution function of the ion species |
\(m^{-6} s^3\) |
|
\(f_{ij}(x_i,x_j)\) |
coefficient in the expansion of \(f\left (x_1,\ldots ,x_d\right )\) |
|
|
\(f_{ce}= \frac {\omega _{ce}}{2\pi }\) |
electron cyclotron frequency |
\(s^{-1}\) |
|
\(f_{ci}= \frac {\omega _{ci}}{2\pi }\) |
ion cyclotron frequency |
\(s^{-1}\) |
|
\(f_{pe}= \frac {\omega _{pe}}{2\pi }\) |
electron plasma frequency |
\(s^{-1}\) |
|
\(f_{pi}= \frac {\omega _{pi}}{2\pi }\) |
ion plasma frequency |
\(s^{-1}\) |
|
\(f_i(x_i)\) |
coefficient in the expansion of \(f\left (x_1,\ldots ,x_d\right )\) |
|
|
\(f\left (x_1,\ldots ,x_d\right )\) |
joint probability distribution |
|
|
\(f^\mathcal {E}\) |
flux term (fieldline integrated source) for plasma energy |
|
|
\(F^\mathcal {E}\) |
flux term (fieldline integrated source divided by field) for plasma energy |
\(m^{-1} s^{-2} C\) |
|
\(f^n\) |
flux term (fieldline integrated source) for plasma number density |
|
|
\(F^n\) |
flux term (fieldline integrated source divided by field) for plasma number density |
\(m^{-3} C\) |
|
\(f^u\) |
flux term (fieldline integrated source) for plasma momentum |
|
|
\(F^u\) |
flux term (fieldline integrated source divided by field) for plasma momentum |
\(m^{-2} s^{-1} C\) |
|
\(f(x,{\bf v},t)\) |
generic distribution function |
\(m^{-6} s^3\) |
|
\(f_{n,Kn}({\bf v})\) |
Knudsen distribution function |
\(m^{-4} s^4\) |
|
\(\Gamma (x)\) |
gamma function of continuous variable \(x\) |
|
|
\(g\) |
factor in (twice) the heat flux |
|
|
\(g(h_j)\) |
activation function (of input \(h_j\)) of a neuron in a neural network |
|
|
\(G\) |
Green’s function |
|
|
\(H_\alpha \) |
Hamiltonian for species \(\alpha \) |
|
|
\(\hat {\boldsymbol {u}}^e\) |
(K+S) Vector of expansion coefficients |
|
|
\(\hat {v}_g\) |
(K+S) Global list of coefficients |
|
|
\(\hat {v}_g\) |
(K+S) List of all elemental coefficients (\(=\underline {v^e}\)) |
|
|
\(h\) |
mesh or inter-node spacing |
\(m\) |
|
\(h_j\) |
real-number input to a neuron in a neural network |
|
|
\(h_p(\xi )\) |
(FE Basis) One-dimensional Lagrange polynomial of order \(p\) |
|
|
\(i\) |
as suffix denotes ions |
|
|
\(i\) |
as suffix denotes regular excited state |
|
|
\(i\) |
as suffix generic label |
|
|
\(I\) |
as suffix labels Monte-Carlo interactions |
|
|
\(I_\phi \) |
\(\phi -\) or toroidal component of plasma current |
\(A\) |
|
\(I_H\) |
Hydrogen reionisation potential as defined in ref. [113] |
\(eV\) |
|
\(i,j,k\) |
(K+S) General summation indices |
|
|
\(^I\mathcal {F}_{i\sigma }\) |
coefficient of ionisation for the transition from metastable state \(\sigma \) to regular excited state \(i\) |
|
|
\(\in \) |
(Sets) Is a member of; belongs to |
|
|
\(I(\psi )=B_T/R\) |
function giving the toroidal field as a function of \(\psi \) |
\(T m^{-1}\) |
|
\(I^Z\) |
power per atom released in dielectronic recombination |
\(W\) |
|
\(j\) |
as suffix is generic label |
|
|
\(j_{ext}(R,Z)\) |
electric current density induced in plasma by external coils |
\(A m^{-2}\) |
|
\(j_\phi \) |
\(\phi -\) or toroidal component of plasma current density |
\(A m^{-2}\) |
|
\(j_{\|}\) |
component of plasma current density parallel to fieldline |
\(A m^{-2}\) |
|
\({\bf j}_{sh}\) |
sheath plasma current density |
\(A m^{-2}\) |
|
\(k\) |
as suffix is generic label |
|
|
\(k\) |
chosen to scale so that \(kT_0\), \(kT_d\) is an energy |
\(?\) |
|
\(\kappa _\alpha \) |
thermal diffusivity of species \(\alpha \) |
\(m^2 s^{-1}\) |
|
\(\kappa _{e\|}\) |
parallel thermal diffusivity of electrons |
\(m^2 s^{-1}\) |
|
\(\kappa _{e\perp }\) |
perpendicular thermal diffusivity of electrons |
\(m^2 s^{-1}\) |
|
\(\kappa _{i\|}\) |
parallel thermal diffusivity of ions |
\(m^2 s^{-1}\) |
|
\(\kappa _{i\perp }\) |
perpendicular thermal diffusivity of ions |
\(m^2 s^{-1}\) |
|
\(\kappa =k_c/\rho _m c_p\) |
thermal diffusivity tensor of solid |
\(m^2 s^{-1}\) |
|
\(k_B\) |
Boltzmann’s constant |
\(J K^{-1}\) |
|
\(k_c\) |
thermal conductivity tensor |
\(J m^{-1} s^{-1} K^{-1}\) |
|
\(K_{cx}\left ( n_i, T_i \right )\) |
reaction rate of charge exchange reactions |
\(m^3 s^{-1}\) |
|
\(K_i\) |
ionization reaction rate |
\(m^3 s^{-1}\) |
|
\(K_{MA}\) |
chosen as \(k_B/m_i\) or \(|e|/m_i\) so that \(\sqrt {K_MT_d}\) is an ion speed |
\(?\) |
|
\(K_M\) |
chosen as \(k_B/m_u\) or \(|e|/m_u\) so that \(\sqrt {K_MT_d/A}\) is an ion speed |
\(?\) |
|
\(K_r\) |
recombination reaction rate |
\(m^3 s^{-1}\) |
|
\(kT_0\) |
\(T_0\) in energy units |
\(J\) |
|
\(kT_d\) |
\(T_d\) in energy units |
\(J\) |
|
\(K_v(x)\) |
modified Bessel function of the second kind, order \(v\) |
|
|
\(k_w\) |
wavenumber vector |
\(m^{-1}\) |
|
\(\lambda \) |
arbitrary quantity |
\(?\) |
|
\(\lambda \) |
Coulomb logarithm |
|
|
\(\lambda \) |
(K+S) Helmholtz equation constant |
|
|
\(\Lambda \) |
Coulomb logarithm |
|
|
\(\lambda _q\) |
\(e\)-folding length of midplane profile of power loss when an exponential is fitted |
\(m\) |
|
\(\Lambda _b\) |
sheath potential drop normalized to \(T_e\) |
\(eV\) |
|
\(\lambda _D\) |
(Glossary) Debye lengthscale above which local electrostatic fluctuations due to presence of discrete charged particles are negligible |
\(m\) |
|
\(\lambda _{mfp,\alpha }\) |
(Glossary) Mean free path of particle species \(\alpha \) |
\(m\) |
|
\(\langle \sigma v \rangle _{CX}\) |
reaction rate for charge exchange |
\(m^3 s^{-1}\) |
|
\(\langle \sigma v \rangle _{ION}\) |
reaction rate for ionisation |
\(m^3 s^{-1}\) |
|
\(\langle \sigma v \rangle _{REC}\) |
reaction rate for recombination |
\(m^3 s^{-1}\) |
|
\(\langle \sigma v\rangle \) |
generic reaction rate |
\(m^3 s^{-1}\) |
|
\(L_0\) |
typical lengthscale |
\(m\) |
|
\(L_i^{N_m}(\boldsymbol {\xi })\) |
(FE Basis) Two-dimensional Lagrange polynomial through \(N_m\) nodes \({\mathbf \xi }_i\) |
|
|
\(L_s\) |
typical lengthscale along fieldline |
\(m\) |
|
\(L_{\|}\) |
connection length of typical fieldline |
\(m\) |
|
\(m\) |
species particle mass |
\(kg\) |
|
\(M_0\) |
Mach number at \(s=0\) boundary |
|
|
\(M_1\) |
Mach number at \(s=1\) boundary |
|
|
\(m_\alpha \) |
mass of species \(\alpha \) |
\(kg\) |
|
\(\mathbb {E}\) |
expectation |
|
|
\(\mathbb {E}_{k\neq i, l\neq j}\) |
expectation computed by integrating over all the \(x_k\) except for \(x_i\) and \(x_j\) |
|
|
\(\mathbb {E}_{x_{k\neq i}}\) |
expectation computed by integrating over all the \(x_k\) except for \(x_i\) |
|
|
\(\mathbb {L}(u)\) |
(K+S) Linear operator in \(u\) |
|
|
\(\mathbb {P}\) |
(K+S) Projection operator |
|
|
\(\mathbb {P}^{\delta }\) |
(K+S) Discrete projection operator |
|
|
\(\mathbf v\) |
(K+S) Velocity \([u, v, w]^T\) |
|
|
\(\mathcal {E}_\alpha \) |
energy of species \(\alpha \) |
\(J m^{-3}\) |
|
\(\mathcal {E}_e\) |
energy of the electrons |
\(J m^{-3}\) |
|
\(\mathcal {E}_i\) |
energy of the ion species |
\(J m^{-3}\) |
|
\(\mathcal {E}_R\) |
total plasma radiation |
\(W m^{-3}\) |
|
\(\mathcal {F}\) |
generic coefficient of excitation, ionisation or recombination |
\(m^3 s^{-1}\) |
|
\(\mathcal {F}_\alpha \) |
functional of moments of species \(\alpha \) |
\(m^{-6} s^3\) |
|
\(\mathcal {I}\) |
(K+S) Interpolation operator |
|
|
\(\mathcal {I}^{\delta }\) |
(K+S) Discrete interpolation operator |
|
|
\(\mathcal {K}_{\|}\) |
parallel thermal conductivity of plasma |
\(m^{-1}s^{-1}\) |
|
\(\mathcal {K}\) |
thermal conductivity of plasma |
\(m^{-1}s^{-1}\) |
|
\(\mathcal {K}_{\perp }\) |
thermal conductivity of plasma perpendicular to field and flux surface |
\(m^{-1}s^{-1}\) |
|
\(\mathcal {K}_{\wedge }\) |
thermal conductivity of plasma perpendicular to field in flux surface |
\(m^{-1}s^{-1}\) |
|
\(\mathcal {L}_7\) |
7-D Lie derivative (space, velocity-space and time make up the \(3+3+1=7\) dimensions) |
\(s^{-1}\) |
|
\(\mathcal {P}_{P}(\Omega )\) |
(K+S) Polynomial space of order \(P\) over \(\Omega \) |
|
|
\(\mathcal {Q}\) |
coefficient in radiation equation |
\(m^3 s^{-1}\) |
|
\(\mathcal {Q}_{\sigma \rightarrow \rho }^{Z\rightarrow Z}\) |
parent-metastable cross-coupling coefficient |
\(m^3 s^{-1}\) |
|
\(\mathcal {S}\) |
coefficient in radiation equation |
\(m^3 s^{-1}\) |
|
\(\mathcal {S}^{Z_m\rightarrow Z}\) |
ionisation coefficient |
\(m^3 s^{-1}\) |
|
\(\mathcal {S}^{Z\rightarrow Z_p}\) |
ionisation coefficient |
\(m^3 s^{-1}\) |
|
\(\mathcal {T}\) |
generic tensor |
\(?\) |
|
\(\mathcal {V}\) |
(K+S) Space of test functions |
|
|
\(\mathcal {V}^{\delta }\) |
(K+S) Finite-dimensional space of test functions |
|
|
\(\mathcal {X}\) |
coefficient in radiation equation |
\(m^3 s^{-1}\) |
|
\(\mathcal {X}_{\sigma \rightarrow \rho }^{Z\rightarrow Z}\) |
generalised collisional-radiative (GCR) excitation coefficient |
\(m^3 s^{-1}\) |
|
\(\mathfrak {R}\) |
Real numbers |
|
|
\(\mathrm {Var}(f)\) |
variance of the distribution of \(f\) computed by integrating over all variables \(x_i\) |
|
|
\(\mathrm {Var}[Q]\) |
variance in random variable \(Q\) |
|
|
\(m_e\) |
mass of electron |
\(kg\) |
|
\(m_i\) |
mass of ion species particle \(m_i= A m_u\) |
\(kg\) |
|
\(m_n\) |
neutral species particle mass |
\(kg\) |
|
\(m_p\) |
mass of proton |
\(kg\) |
|
\(m_u\) |
atomic mass unit |
\(1.6605 \times 10^{-27}\,kg\) |
|
\(M_s\) |
Mach number, allowed to take either sign |
|
|
\(M_S\) |
number of energy states of an atom |
|
|
\(\mu , \nu \) |
(K+S) Dynamic, kinematic viscosities |
|
|
\(\mu _{cx}=\omega _c/\nu _{cx}\) |
measures strength of magnetization with respect to charge exchange reaction |
|
|
\(\mu _m\) |
reduced mass of two particles |
\(kg\) |
|
\(M_Z\) |
number of metastable states for species \(\alpha \) (which includes the ground state) |
|
|
\(n\) |
number density |
\(m^{-3}\) |
|
\(n_{ref}\) |
reference number density of the plasma ions |
\(m^{-3}\) |
|
\(N_{ref} \) |
normalising or reference number density |
\(10^{18}\) |
|
\(N\) |
number density, may be scaled by \(N_{ref}=10^{18}\) |
\(m^{-3}\) |
|
\(n_0\) |
initial number density |
\(m^{-3}\) |
|
\(\nabla \cdot \) |
(K+S) Divergence |
|
|
\(\nabla \times \) |
(K+S) Curl |
|
|
\(\nabla ^2\) |
(K+S) Laplacian |
|
|
\(N_{b}\) |
(K+S) Number of global boundary degrees of freedom |
|
|
\(n_B=N/B\) |
number density divided by field strength |
\(m^{-3}T^{-1}\) |
|
\(N_D\) |
Number of degrees of freedom per dimension, \(D=1,2,\ldots 6\) |
|
|
\(N_{dof}\) |
(K+S) Number of global degrees of freedom |
|
|
\(n_{con}\) |
blob contrast factor |
|
|
\(n_e\) |
number density of the electrons |
\(m^{-3}\) |
|
\(N_{el}\) |
(K+S) Number of finite elements |
|
|
\(N_{eof}\) |
(K+S) Total number of elemental degrees of freedom \(N_{eof} \simeq N_{el}N_m\) |
|
|
\(n_i\) |
number density of the plasma ions |
\(m^{-3}\) |
|
\(n_j({\bf x},t)\) |
member of the set of deterministic coefficients of the “random trial basis" |
|
|
\(N_{m}\) |
(K+S) Number of elemental degrees of freedom |
|
|
\(n_n\) |
neutral density |
\(m^{-3}\) |
|
\(\notin \) |
(Sets) Is not a member of; does not belong to |
|
|
\(\not \subset \) |
(Sets) Is not a subset of |
|
|
\(n_p\) |
number density of the plasma ions |
\(m^{-3}\) |
|
\(N_{Q}\) |
(K+S) Total number of quadrature points \(N_Q = Q_1 Q_2 Q_3\) |
|
|
\(n_s\) |
number density of isotope \(s\) |
\(m^{-3}\) |
|
\(N_s\) |
number density of isotope \(s\) |
\(m^{-3}\) |
|
\(N_T\) |
number of samples in temperature used to define typically a crossection in the ADAS database refs. [114, 115] |
|
|
\(\nu \) |
plasma kinematic viscosity |
\(m^2 s^{-1}\) |
|
\(\nu _\alpha \) |
kinematic viscosity of species \(\alpha \) |
\(m^2 s^{-1}\) |
|
\(\nu _{cx}=K_{cx} n_n\) |
charge exchange ‘frequency’ |
\(s^{-1}\) |
|
\(\nu _{e0}\) |
electron kinematic viscosity caused by neutrals |
\(m^2 s^{-1}\) |
|
\(\nu _{e\|}\) |
parallel kinematic viscosity of electrons |
\(m^2 s^{-1}\) |
|
\(\nu _{e\perp }\) |
perpendicular kinematic viscosity of electrons |
\(m^2 s^{-1}\) |
|
\(\nu _{i\|}\) |
parallel kinematic viscosity of ions |
\(m^2 s^{-1}\) |
|
\(\nu _i\) |
ion kinematic viscosity |
\(m^2 s^{-1}\) |
|
\(\nu _{i0}\) |
ion kinematic viscosity caused by neutrals |
\(m^2 s^{-1}\) |
|
\(\nu _{i\perp }\) |
perpendicular kinematic viscosity of ions |
\(m^2 s^{-1}\) |
|
\(\nu ^{*}_\alpha \) |
(Glossary) Normalised collision frequency for species \(\alpha \) |
|
|
\(\nu ^{*}_c = \frac {q_e^4}{3 m_p^2\epsilon _0^2} L_0 n_0 /C_0^4\) |
Collisionality parameter |
|
|
\(\nu _\alpha \) |
(Glossary) Collision frequency for species \(\alpha \) |
\(s^{-1}\) |
|
\(\nu _{\alpha {\sf n}}\) |
Collision frequency for species \(\alpha \) with neutrals |
\(s^{-1}\) |
|
\(\nu _{\alpha \beta }\) |
Collision frequency for species \(\alpha \) with species \(\beta \) |
\(s^{-1}\) |
|
\(n^Z\) |
number density for charge state \(Z\) |
\(m^{-3}\) |
|
\(N_P\) |
number of particles in a calculation |
|
|
\(N_{P\alpha } \) |
number of particles of species \(\alpha \) in a calculation |
|
|
\(N_Z\) |
number of charge states for an ion species |
|
|
\(n^Z_i\) |
number density for charge state \(Z\), excited state \(i\) |
\(m^{-3}\) |
|
\(n^Z_\sigma \) |
number density for charge state \(Z\), metastable state \(\sigma \) |
\(m^{-3}\) |
|
\(\omega _{ce}= |e|B/m_e\) |
electron cyclotron angular frequency |
\(radians s^{-1}\) |
|
\(\omega _{ci}= Z_i e B/m_i\) |
ion cyclotron angular frequency |
\(radians s^{-1}\) |
|
\(\omega _{pe}= \sqrt {\frac {nq_e^2}{\epsilon _0 m_e}}\) |
plasma angular frequency for electrons |
\(radians s^{-1}\) |
|
\(\omega _{pi}= Z_i\sqrt {\frac {nq_e^2}{\epsilon _0 m_i}}\) |
plasma angular frequency for ions |
\(radians s^{-1}\) |
|
\(\Omega \) |
(K+S) Solution domain |
|
|
\(\Omega ^e\) |
(K+S) Elemental region |
|
|
\(\mathrm {p}(A|B)\) |
conditional probability of event \(A\) given event \(B\) is known or assumed to have occurred |
|
|
\(p_\alpha \) |
pressure of species \(\alpha \) |
\(N m^{-2}\) |
|
\(\parallel Q \parallel _E \) |
the ‘energy’ norm |
|
|
\((\partial f/\partial t)_C\) |
source in Boltzmann due to inter-particle interactions |
\(m^{-6} s^2\) |
|
\(\partial \Omega _e\) |
(K+S) Boundary of \(\Omega ^e\) |
|
|
\(\partial \Omega \) |
(K+S) Boundary of \(\Omega \) |
|
|
\(\partial \Omega _{\mathcal D}\) |
(K+S) Domain boundary with Dirichlet conditions |
|
|
\(\partial \Omega _{\mathcal N}\) |
(K+S) Domain boundary with Neumann conditions |
|
|
\(P_C\) |
number of modes in basis for polynomial chaos |
|
|
\(p_e\) |
pressure of the electrons |
\(N m^{-2}\) |
|
\(\phi \) |
angle in toroidal direction |
radians \(^c\) |
|
\(\Phi \) |
electr(ostat)ic potential |
\(V\) |
|
\(\phi _{pq}, \phi _{pqr}\) |
(FE Basis) Expansion basis |
|
|
\(\phi _{e,\xi }\) |
(FE Basis) expansion basis as a function of global position \(\bf x\) |
|
|
\(p\) |
(K+S) pressure |
\(N m^{-2}\) |
|
\(p = \sum _\alpha n_\alpha kT_\alpha \) |
plasma pressure |
\(N m^{-2}\) |
|
\(p\) |
as suffix labels (super-)particles |
|
|
\(p_i\) |
pressure of the ion species |
\(N m^{-2}\) |
|
\(P_i\) |
(FE Basis) Polynomial order in the \(i\)th direction |
|
|
\(p(\psi )\) |
function giving the pressure as a function of \(\psi \) of the magnetic flux |
\(N m^{-2}\) |
|
\(p,q,r\) |
(K+S) General summation indices |
|
|
\(Pr\) |
Prandtl number |
|
|
\(Pr_M\) |
magnetic Prandtl number |
|
|
\(\psi \) |
poloidal magnetic flux |
\(T m^2\) |
|
\(\psi ^a_p, \psi ^b_{pq}, \psi ^c_{pqr}\) |
(FE Basis) Modified principal functions |
|
|
\(\Psi _i\) |
\(i^{th}\) member of a set of basis functions, typically multi-dimensional Hermite polynomials |
|
|
\(P(T)\) |
emitted power integrated over all wavelengths |
\(W m^3\) |
|
\(\mathrm {p}(x)\) |
probability distributions |
|
|
\(P(x)\) |
Cumulant probability distribution |
|
|
\(P^Z\) |
radiated power per atom of \(n^Z\) |
\(W\) |
|
\(Q_\|\) |
combined energy flux at a boundary |
\(J m^{-2} s^{-1}\) |
|
\(q_\alpha \) |
charge on a particle of species \(\alpha \) |
\(C\) |
|
\(q_e\) |
charge on an electron, negative by convention |
\(C\) |
|
\(Q(f_\alpha , f_\beta )\) |
Boltzmann collision operator |
\(m^{-6} s^2\) |
|
\(Q_H\) |
cooling rate due to excitation as defined in ref. [113] |
\(K m^{-3} s^{-1}\) |
|
\(q_i\) |
charge on an ion |
\(C\) |
|
\(q_{\|e}\) |
electron energy flux along fieldline |
\(J m^{-2} s^{-1}\) |
|
\(q_{\|i}\) |
ion energy flux along fieldline |
\(J m^{-2} s^{-1}\) |
|
\({\bf q}_e\) |
electron energy flux |
\(J m^{-2} s^{-1}\) |
|
\({\bf q}_i\) |
ion energy flux |
\(J m^{-2} s^{-1}\) |
|
\(Q_i\) |
(FE Basis) Quadrature order in the \(i\)th direction |
|
|
\(Q_{ie}\) |
collisional energy equipartition term |
\(kg m^{-1} s^{-3}\) |
|
\(r\) |
order of higher order term |
|
|
\(r_0\) |
radius used in initial condition, such as blob size |
\(m\) |
|
\(R\) |
cylindrical coordinate |
\(m\) |
|
\(R_0\) |
major radius of torus |
\(m\) |
|
\(R_p\) |
recycling coefficient for particles |
|
|
\(R_E\) |
recycling coefficient for particle energy |
|
|
\(\rho \) |
as suffix is label of metastable state |
|
|
\(\rho \) |
(K+S) Density |
|
|
\(\rho _c=\sum _\alpha Z_\alpha |e| n_\alpha \) |
charge density of the medium |
\(C m^{-3}\) |
|
\(\rho _m=\sum _\alpha A_\alpha m_u n_\alpha \) |
mass density of the medium |
\(kg m^{-3}\) |
|
\(\rho _{t\alpha }\) |
(Glossary) Gyroradius or Larmor radius of orbit of charged particle of species \(\alpha \) about magnetic field direction |
\(m\) |
|
\(^R\mathcal {F}_{i\sigma }\) |
coefficient of recombination for the transition from metastable state \(\sigma \) to regular excited state \(i\) |
|
|
\(s_{\|}\) |
arclength along fieldline |
\(m\) |
|
\(s\) |
as suffix, isotope label (\(\alpha \) preferred for species) |
|
|
\(s\) |
parameterises distance along the fieldline \(0\leq s \leq 1\) |
|
|
\(S_\alpha \) |
source term in Boltzmann equation for species \(\alpha \) |
\(m^{-6} s^2\) |
|
\(S_C\) |
total source term in Boltzmann equation |
\(m^{-6} s^2\) |
|
\(S_\mathrm {ana}({\bf x},t)\) |
explicit/analytic source term in fluid equation(s) |
\(m^{-3} s^{-1}\) ? |
|
\(S^n_\mathrm {ana}({\bf x},t)\) |
numerically convenient source term in fluid equation(s) |
\(m^{-3} s^{-1}\) ? |
|
\(S_{exp}({\bf x}, {\bf v},t)\) |
explicit source term in Boltzmann equation |
\(m^{-6} s^2\) |
|
\(\sf n\) |
neutral density |
|
|
\(\sf T\) |
neutral temperature |
|
|
\(\sf u\) |
neutral velocity |
|
|
\(s_i\) |
arclength parameter for boundary (\(i=1\) inner, \(i=2\) outer) |
|
|
\(s^\mathcal {E}\) |
source term in plasma energy equation |
|
|
\(s^{\mathcal {E}}_{e}\) |
energy density source term for electrons |
|
|
\(s^{\mathcal {E}}_{i}\) |
energy density source term for ions |
|
|
\(s^\mathcal {E}_n\) |
source term in neutral energy equation |
|
|
\(s^\mathcal {E}_{\perp e}\) |
energy cross-field source term for electrons |
|
|
\(s^\mathcal {E}_{\perp i}\) |
energy cross-field source term for ions |
|
|
\(s^\mathcal {E}_{\perp n}\) |
energy cross-field source term for neutrals |
|
|
\(s^n\) |
source term in plasma density equation |
|
|
\(s^n_n\) |
source term in neutral density equation |
|
|
\(s^n_{e}\) |
number density source term for electrons |
|
|
\(s^n_{i}\) |
number density source term for ions |
|
|
\(s^u\) |
source term in plasma momentum equation |
|
|
\(s^u_n\) |
source term in neutral momentum equation |
|
|
\(s^u_{\perp n}\) |
momentum cross-field source term for neutrals |
|
|
\(S_i\) |
Sobol sensitivity index, gives a normalised measure of the sensitivity of the distribution of \(f\) to the parameter \(x_i\) |
|
|
\(\sigma \) |
as suffix labels metastable state |
|
|
\(\sigma \) |
reaction cross-section |
\(m^2\) |
|
\(\sigma _C\) |
reaction rate for charge exchange |
|
|
\(\sigma _E\) |
cooling rate due to excitation |
|
|
\(\sigma _E\) |
electrical conductivity |
\(\Omega ^{-1} m^{-1}\) |
|
\(\sigma _I\) |
reaction rate for ionisation |
|
|
\(\sigma _s^{i|0}\) |
collision cross-section for ions with neutrals |
\(m^2\) |
|
\(\sigma _s^{e|0}\) |
collision cross-section for electrons with neutrals |
\(m^2\) |
|
\(S_{ij}\) |
Sobol sensitivity index, gives a normalised measure of the sensitivity of the distribution of \(f\) to the parameters \(x_i\) and \(x_j\) |
|
|
\(S^\mathcal {E}\) |
source term in plasma energy equation |
\(kg m^{-1} s^{-3}\) |
|
\(S^{\mathcal {E}}_{e}\) |
energy density source term for electrons |
\(kg m^{-1} s^{-3}\) |
|
\(S^{\mathcal {E}}_{i}\) |
energy density source term for ions |
\(kg m^{-1} s^{-3}\) |
|
\(S^\mathcal {E}_n\) |
source term in neutral energy equation |
\(kg m^{-1} s^{-3}\) |
|
\(S^\mathcal {E}_{\perp e}\) |
energy cross-field source term for electrons |
\(kg m^{-1} s^{-3}\) |
|
\(S^\mathcal {E}_{\perp i}\) |
energy cross-field source term for ions |
\(kg m^{-1} s^{-3}\) |
|
\(S^\mathcal {E}_{\perp n}\) |
energy cross-field source term for neutrals |
\(kg m^{-1} s^{-3}\) |
|
\(S^n\) |
source term in plasma density equation |
\(m^{-3} s^{-1}\) |
|
\(S^n_{e}\) |
number density source term for electrons |
\(m^{-3} s^{-1}\) |
|
\(S^n_{i}\) |
number density source term for ions |
\(m^{-3} s^{-1}\) |
|
\(S^n_n\) |
source term in neutral density equation |
\(m^{-3} s^{-1}\) |
|
\(S^n_{\perp n}\) |
number density cross-field source term for neutrals |
\(m^{-3} s^{-1}\) |
|
\(S^n_{\perp }\) |
number density cross-field source term for plasma |
\(m^{-3} s^{-1}\) |
|
\(S_{\perp n}\) |
generic cross-field source term for neutrals |
\(m^{-3} s^{-1}\) |
|
\(S^u\) |
source term in plasma momentum equation |
\(kg m^{-2} s^{-2}\) |
|
\(\subset \) |
(Sets) Is a subset of |
|
|
\(S^u_n\) |
source term in neutral momentum equation |
\(kg m^{-2} s^{-2}\) |
|
\(S^u_{\perp n}\) |
momentum cross-field source term for neutrals |
\(kg m^{-2} s^{-2}\) |
|
\(S^Z_\rho \) |
particle source for ion of metastable state \(\sigma \) (species \(\alpha \)) with charge state \(Z\) |
\(m^{-3} s^{-1}\) |
|
\(S^Z_\alpha \) |
particle source for ion of species \(\alpha \) with charge state \(Z\) |
\(m^{-3} s^{-1}\) |
|
\(t\) |
time usually in seconds |
\(s\) |
|
\(t'\) |
offset time usually in seconds |
\(s\) |
|
\(T\) |
plasma temperature |
\(eV\) |
|
\(t_0\) |
characteristic evolutionary timescale usually in seconds |
\(s\) |
|
\(t_s\) |
characteristic timescale usually in seconds |
\(s\) |
|
\(t_H\) |
Numerical hand-off time interval usually in seconds |
\(s\) |
|
\(t_R\) |
Numerical ramp-up time interval usually in seconds |
\(s\) |
|
\(T_0\) |
initial temperature (prefixed by \(k\) implies energy in SI) |
\(eV\) |
|
\(T_{Kn}\) |
reference temperature of Knudsen distribution (prefixed by \(k\) implies energy in SI) |
\(eV\) |
|
\(T_{ref}\) |
reference temperature (prefixed by \(k\) implies energy in SI) |
\(eV\) |
|
\(T_s\) |
characteristic temperature (\(T_s=(L_s/t_s)^2/K_M\)) |
\(eV\) |
|
\(T_\alpha \) |
temperature of species \(\alpha \) |
\(eV\) |
|
\(\tau \) |
optical depth |
\(m\) |
|
\(\tau _\alpha \) |
collision or relaxation time of species \(\alpha \) |
\(s\) |
|
\(\tau _e\) |
electron collision or relaxation time |
\(s\) |
|
\(\tau _i\) |
ion species collision or relaxation time |
\(s\) |
|
\(\tau _{e{\sf n}} \) |
electron-neutral collision time |
\(s\) |
|
\(\tau _{i{\sf n}} \) |
ion species-neutral collision time |
\(s\) |
|
\(\tau _{ce}=1/f_{ce}\) |
electron cyclotron timescale |
\(s\) |
|
\(\tau _{ci}=1/f_{ci}\) |
ion cyclotron timescale |
\(s\) |
|
\(\tau _{pe}=1/f_{pe}\) |
plasma timescale for electrons |
\(s\) |
|
\(\tau _{pi}=1/f_{pi}\) |
plasma timescale for ions |
\(s\) |
|
\(\tau _{\mathcal {E}_e}\) |
loss time of energy density for electrons |
\(s\) |
|
\(\tau _{\mathcal {E}_i}\) |
loss time of energy density for ions |
\(s\) |
|
\(\tau _{n_e}\) |
loss time of number density for electrons |
\(s\) |
|
\(\tau _{n_i}\) |
loss time of number density for ions |
\(s\) |
|
\(T_d=T_i+T_e\) |
combined temperature of the electrons and ions |
\(eV\) |
|
\(T_e\) |
electron temperature (prefixed by \(k\) implies energy in SI) |
\(eV\) |
|
\(T_H\) |
the Hydrogen reionisation potential |
|
|
\(\theta \) |
angular coordinate |
radians \(^c\) |
|
\(\theta \) |
random parameter \(0\leq \theta \leq 1\) |
|
|
\(T_i\) |
ion temperature |
\(eV\) |
|
\(\tilde {a}\) |
scaled matrix coefficient |
|
|
\(\tilde {b}=B/B_0\) |
dimensionless magnetic field |
|
|
\(\tilde {\psi }^a_p, \tilde {\psi }^b_{pq}, \tilde {\psi }^c_{pqr}\) |
(FE Basis) Orthogonal principal functions |
|
|
\(u\) |
generic first velocity component |
\(m s^{-1}\) |
|
\(U\) |
velocity component (flow) along fieldline |
\(m s^{-1}\) |
|
\(U_\alpha \) |
velocity component (flow) along fieldline of species \(\alpha \) |
\(m s^{-1}\) |
|
\(U_d =L_s/t_0\) |
speed measuring the importance of the transient term |
\(m s^{-1}\) |
|
\(U_s =L_s/t_s\) |
characteristic speed |
\(m s^{-1}\) |
|
\(U_A\) |
Alfvén speed |
\(m s^{-1}\) |
|
\(\underline {\boldsymbol {f}^e}\) |
(K+S) Concatenation of elemental vector \(\boldsymbol {f}^e\) |
|
|
\(\underline {\boldsymbol {W}^e}\) |
(K+S) Block-diagonal extension of matrix \(\boldsymbol {W}^e\) |
|
|
\(u_R=1/R\) |
Radial component of Grad-Shafranov ‘flow’ |
|
|
\(v\) |
generic second velocity component |
\(m s^{-1}\) |
|
\(v_{\|}\) |
fluid velocity component along fieldline |
\(m s^{-1}\) |
|
\(V^e\) |
spatial volume occupied by finite element \(e\) |
\(m^3\) |
|
\(V_i\) |
variance of the distribution of \(f\) as the parameter \(x_i\) varies |
|
|
\(V_{ij}\) |
variance of the distribution of \(f\) as the parameters \(x_i\) and \(x_j\) vary |
|
|
\(w\) |
generic third velocity component |
\(m s^{-1}\) |
|
\(w_{jk}\) |
weight in neural network indexed by neuron \(j\) and input \(k\) |
|
|
\(w_p\) |
weight of particle \(p\) |
|
|
\(w_{\alpha ,ref}\) |
normalising or reference weight of particle of species \(\alpha \) |
|
|
\(w_{ref} \) |
normalising or reference number for superparticles |
\(10^{10}\) |
|
\(W\) |
weighting function for particle-in-cell |
|
|
\(x\) |
Cartesian coordinate |
\(m\) |
|
\(x_0\) |
coordinate value used in specifying initial condition, eg. blob position |
\(m\) |
|
\(x_1, x_2, x_3, {\mathbf x}\) |
(FE Basis) Global Cartesian coordinates |
|
|
\(x_\alpha \) |
collisionality factor of species \(\alpha \) |
|
|
\(x_e = \omega _{ce}\tau _e\) |
collisionality factor of electrons |
|
|
\(x_i = \omega _{ci}\tau _i\) |
collisionality factor of ions |
|
|
\(x_i\) |
generic parameter or variable |
|
|
\(\xi _1, \xi _2, \xi _3, \boldsymbol {\xi }\) |
(FE Basis) Local Cartesian coordinates |
|
|
\(\xi _i\) |
random number within the unit interval \([0,1]\) |
|
|
\(^X\mathcal {F}_{i\sigma }\) |
coefficient of excitation for the transition from metastable state \(\sigma \) to regular excited state \(i\) |
|
|
\(y\) |
Cartesian coordinate |
\(m\) |
|
\(y_0\) |
coordinate value used in specifying initial condition, eg. blob position |
\(m\) |
|
\(z\) |
Cartesian coordinate |
\(m\) |
|
\(z_0\) |
coordinate value used in specifying initial condition |
\(m\) |
|
\(Z\) |
Cartesian coordinate |
\(m\) |
|
\(Z\) |
charge state of the ion |
|
|
\(Z\) |
cylindrical coordinate |
\(m\) |
|
\(Z_0(\alpha )\) |
number of charge states of species \(\alpha \) included in the model |
|
|
\(Z_a\) |
Gaussian random process, index \(a\) |
|
|
\(\zeta \) |
magnetic Prandtl number as defined in Cambridge |
|
|
\(\zeta =-\phi \) |
toroidal angle coordinate |
radians \(^c\) |
|
\(Z_{eff}\) |
effective charge state of plasma ions |
|
|
\(Z_i\) |
charge state of ion |
|
|
\(Z_\alpha \) |
charge state of ion species \(\alpha \) |
|
|
\(Z_m=Z-1\) |
where \(Z\) is ion charge state |
|
|
\(Z_p=Z+1\) |
where \(Z\) is ion charge state |
|
|
\(Z_{sum}=\sum _\alpha Z_0(\alpha )\) |
where \(Z_0\) is number of charge states of species \(\alpha \) |
|