# XYLENE POWER LTD.

## PLASMA IMPACT FUSION GLOSSARY

#### By Charles Rhodes, P. Eng., Ph.D.

INTRODUCTION:
This web page provides a glossary of symbols used on this web site for mathematical description of the Plasma Impact Fusion (PIF) process.
It may be helpful for persons studying the PIF process to print a copy of this web page.

Af = angle in radians measured at (0, 0) between the spheromak equatorial plane and (Rf, Hf)
As = outside surface area of a spheromak plasma sheet
Av = surface area of enclosed volume
B = magnetic field strength
Ba = axial magnetic field strength at (0,0)
Bh = magnetic field around plasma hose due to current Ih
Bp = poloidal magnetic field strength
Bpo = poloidal magnetic field strength in spheromak core at (0, 0)
Bpc = poloidal magnetic field strength in spheromak core at (Rc, 0)
Bpf = poloidal magnetic field strength outside spheromak surface at (Rf, Hf)
Bps = poloidal magnetic field strength outside spheromak surface at (Rs, 0)
Bptc = 0 = poloidal magnetic field in toroidal region at (Rc, 0)
Bpts = 0 = poloidal magnetic field in toroidal region at (Rs, 0)
Bps = poloidal magnetic field strength outside spheromak surface at (Rs, 0)
Bt = toroidal magnetic field strength
Btc = 0 toroidal magnetic field strength inside spheromak core at (Rc, 0)
Btos = 0 toroidal magnetic field strength outside spheromak at (Rs, 0)
Btts = toroidal magnetic field strength inside toroidal region at (Rs, 0)
Bttc = toroidal magnetic field strength inside toroidal region at (Rc, 0)
Btf = toroidal magnetic field strength inside spheromak surface at (Rf, Hf)
Btts = toroidal magnetic field strength inside spheromak surface at (Rs, 0)
C = speed of light
Ch = charge propagation velocity along a plasma hose
Dh = plasma hose center to center spacing
Dhc = value of Dh at (Rc, 0)
Dhf = value of Dh at (Rf, Hf)
Dhp = spacing between effective poloidal plasma hoses
Dht = spacing between effective toroidal plasma hoses
Dhs = vlue of Dh at (Rs, 0)
E = electric field strength (depends on context)
E = energy (depends on context)
Ebl = Elb = liquid lead binding energy per atom
Ee = electric field energy of a spheromak (rely on context)
Ee = gross electrical energy (rely on context)
Eep = electric field energy within a spheromak poloidal region
Eet = electric field energy within a spheromak toroidal region
Efs = spherical field energy for 0 < R < infinity
Efst = field energy of sphere that occurs inside toroidal plasma sheet
Eft = cylindrical field energy inside toroidal plasma sheet
Eki = ion kinetic energy
Ekif = ion kinetic energy at T = Tf, Ri = Rif
Ekig = ion kinetic energy at T = Tg, Ri = Rig, Ep = (Ekld / 4)
Ekih = ion kinetic energy at T = Th, Ri = Rih, Ep = (Ekld / 2)
Ekii = ion kinetic energy at T = Ti, Ri = Rii, Ep = Ekld
Ekij = ion kinetic energy at T = Tj, Ri = Rij, Ep = (Ekld / 2)
Ekik = ion kinetic energy at T = Tk, Ri = Rik, Ep = (Ekld / 4)

Ekd = deuterium ion kinetic energy
Ekdg = deuterium ion kinetic energy at Ri = Rig
Ekdh = deuterium ion kinetic energy at Ri = Rih
Ekdi = deuterium ion kinetic energy at Ri = Rii

Ekdw = deuterium ion kinetic energy at liquid lead wall
Eke = electron kinetic energy in a spheromak
Ekea = initial free electron kinetic energy
Ekeb = final free electron kinetic energy
Eket = component of Eke due to toroidal particle motion

Ekl = kinetic energy of liquid lead
Ekld = kinetic enegy of liquid lead at shell formation
Eklf = = kinetic energy of liquid lead at beginning of adiabatic compression
Eklg = = kinetic energy of liquid lead at fusion ignition

Ekn = kinetic energy of neutral particle
Ekna = Enka = kinetic energy of neutral particle at Ri = Ria
Eknb = Enkb = kinetic energy of neutral particle at Ri = Rib

Ekt = tritium ion kinetic energy
Ekth = tritium ion kinetic energy at Ep = Ekld / 2

Em = magnetic field energy of a spheromak
Emp = poloidal magnetic field energy of a spheromak
Emt = toroidal magnetic field energy of a spheromak
Eoa = electric field outside the spheromak at the up stream end of the plasma injector
Eob = electric field outside the spheromak at the down stream end of the plasma injector

Ep = random plasma thermal energy
Epf = random plasma thermal energy at T = Tf, Ri = Rif = 1.0 m, full ionization and particle energy redistribution
Epg = random plasma thermal energy at T = Tg, Ri = Rig, Epg = (Ekld / 4)
Eph = random plasma thermal energy at T = Th, Ri = Rih, Eph = (Ekld / 2)
Epi = random plasma thermal energy at T = Ti, Ri = Rii, Epi = Ekld

Ep = particle potential energy
Epa = particle potential energy at T = Ta
Epb = particle potential energy at T = Tb
Epbf = fixed component of Epb
Epbv = variable component of Epb
Epc = particle potential energy at T = Tc
Epo = plasma energy at Ep = (Ekla / 2)
Epsilon = 8.85 X 10^-12 (coul^2 s^2) / (kg m^3) = permittivity of free space
Epulse = fusion energy release = 600 MJ
Ercc = 0 = radial electric field in spheromak core
Ertc = radial electric field in toroidal region at (Rc,0)
Erts = radial electric field in toroidal region at (Rs, 0)
Eros = radial electric field in outside region at (Rs, 0)
Es = radial electric field strength at spheromak outside surface
Esa = value of Es before spheromak compression
Esb = value of Es after spheromak compression
Et = total particle energy
Et = gross thermal energy (rely on context)
Eta = total particle energy at T = Ta
Etb = total particle energy at T = Tb
Etc = total particle energy at T = Tc (rely on context)
Ett = total field energy of a spheromak
Etta = total field energy of a spheromak before compression
Ettb = total field energy of a spheromak after compression
Et = total particle energy
Eta = value of Et at T = Ta
Etb = value of Et at T = Tb
Etc = value of Et at T = Tc
Ew = radial electric field on spheromak equatorial plane at inside surface of enclosure wall
Ewa = value of Ew at T = Ta (uncompressed spheromak)
Ewb = value of Ew at T = Tb (compressed spheromak)
Ewm = maximum permitted value of Ew due to field emission
Ex = 2.71828
Fc = Ekld / (electrical energy used for liquid lead acceleration)
Fg = (Ni / Nno) = ion gun efficiency (rely on context)
Fg = (Ee / Et) = turbogenerator efficiency
Fh = characteristic frequency of a plasma hose
Fha = initial value of Fh
Fhb = final value of Fh
Fp = poloidal current frequency

Fr = fraction of injected deuterium atoms that have fused
Frf = 0
Frg = 0
Fri = Fr evaluated at plasma radius of maximum compression where Ri = Rii
Frk = Fr evaluated at Ri = Rik

Ft = toroidal current frequency
G = (Rwb / Rwa) = 5 = plasma injector gain
Gt = number of tritium atoms produced per neutron emitted by D-T reaction
h = 6.62 X 10^-34 kg m^2 / s = Planck Constant
H = distance from the equatorial plane of a spheromak
Hc = maximum distance of spheromak plasma sheet from the equatorial plane at R = Rc
Hf = maximum value of H for the plasma sheet which occurs at R = Rf
Hfa = value of Hf before spheromak compression
Hfb = value of Hf after spheromak compression
Ih = plasma hose current
Ir = plasma ribbon current
Irp = plasma ribbon current poloidal component
Irpc = value of Irp at (Rc, 0)
Irps = value of Irp at (Rs, 0)
Irt = plasma ribbon current toroidal component
Irtc = value of Irt at (Rc, 0)
Irts = value of Irt at (Rs, 0)
Lh = Nt Lrb = length of plasma hose
Lp = length of a purely poloidal spheromak plasma hose turn
Lpa = 2 Pi (Rs Rc)^0.5 = effective length of a poloidal plasma hose turn
Lpc = value of Lp at point (Rc, 0)
Lpf = 2 Pi Rf = geometrical value of Lp at R = Rf
Lps = value of Lp at point (Rs, 0)
Lr = Lpa / Lt = spheromak shape ratio
Lrb = length of plasma ribbon
Lt = length of purely toroidal spheromak plasma hose turn
Md = rest mass of deuterium ion
Me = 9.109 X 10^-31 kg = rest mass of an electron
Mi = rest mass of an ion
Ml = rest mass of a lead atom
Mn = rest mass of neutral gas molecule
Mp = 1.67 X 10^-27 kg = rest mass of a proton
Mt = rest mass of a tritium ion
Mu = 4 Pi X 10^-7 T^2 m^3 / J = permiability of free space

Nd = number of deuterium ions present in plasma
Ndf = value of Nd at T = Tf
Ndg = value of Nd at T = Tg
Ndh = value of Nd at T = Th
Ndi = value of Nd at T = Ti
Ndj = value of Nd at T = Tj
Ndk = value of Nd at T = Tk

Ne = number of free electrons in a spheromak
Nea = value of Ne before spheromak compression
Neb = value of Ne after spheromak compression
Nf = number of D atoms in the reaction chamber
Ni = number of ions in a spheromak
Nid = number of deuterium ions
Nit = number of tritium ions
Nm = 21.280 X 10^19 = number of hydrogen isotope molecules that fuse during a fusion pulse
Nn = number of neutral gas molecules per m^3
Nno = number of neutral atoms injected into vacuum chamber to form spheromak
Nnoi = number of neutral atoms of species "i".
Np = number of poloidal plasma hose turns in a spheromak
Nr = (Np / Nt)
Nt = number of toroidal plasma hose turns in a spheromak
Nt = number of tritium ions present in plasma
Pi = 3.14159
Phis = spheromak surface potential
Q = 1.602 X 10^-19 coulombs = proton charge
Qs = net charge on a spheromak
R = radial distance from the main axis of symmetry of a spheromak
Rc = spheromak core radius on the equatorial plane
Rca = value of Rc before spheromak compression
Rcb = value of Rc after spheromak compression
Re = electron path radius of curvature
Rf = spheromak funnel radius at H = Hf
Rfa = value of Rf before spheromak compression
Rfb = value of Rf after spheromak compression
Rh = radial distance from the axis of a plasma hose
Rhoh = charge per unit length on plasma hose
Rhol = 10.66 X 10^3 kg / m^3 = density of liquid lead alloy
Rhow = density of lead at wall at end of adiabatic compression
Ri = ion path radius of curvature
Ri = liquid lead sphere inside radius
Ria > Rib > Ric > Rid > Rie > Rif > Rig > Rih > Rii
Rii < Rij < Rik
Ria = Value of Ri when liquid lead guns are ready to fire;
Rib = value of Ri when liquid lead reaches its maximum velocity within the gun barrel
Ric = value of Ri when liquid lead reaches the gun muzzle;
Rid = 1.45 m = value of Ri when liquid lead forms a closed spherical shell;
Rie = value of Ri when fuel injection is complete;
Rif = value of Ri when random plasma is fully ionized;
Rig = value of Ri when Ep = (Ekld / 4);
Rih = value of Ri when Ep = (Ekld / 2);
Rii = value of Ri when Ep = Ekld;
Rij = value of Ri when Ep = (Ekld / 2);
Rik = value of Ri when Ep = (Ekld / 4);

Ro = liquid lead sphere outside radius
Rod = value of Ro at state "d"
Rob = 0.3 m = value of Ro at state "g"
Rpa = (Lpa / 2 Pi) average radius of spheromak poloidal turns
Rs = radius of spheromak outside wall on the equatorial plane
Rsa = value of Rs before spheromak compression
Rsb = value of Rs after spheromak compression
Rsl = value of Rs observed when spheromak is inside a cylindrical metal enclosure
Rw = inside radius of a cylindrical vacuum enclosure wall used to contain a spheromak
Rwa = 1.5 m = inside radius of charge injector at its upstream end
Rwb = 0.3 m = inside radius of charge injector at its downstream end
Rx = plasma sheet radius of curvature at (Rf, Hf)
Sa = net charge per unit area on a plasma sheet
Sac = value of Sa at (Rc, 0)
Sas = value of Sa at (Rs, 0)
Sigma = 3 X 10^-28 m^2 = average D-T fusion cross section for 60 keV < Eki < 240 keV
Sigmaa = electron impact ionization cross section at state "a"
Sigmab = electron impact ionization cross section at state "b"
Sigmac = electron impact ionization cross section at state "c"

T = time (rely on context for meaning)
Ta < Tb < Tc < Td < Te < Tf < Tg < Th < Ti < Tj < Tk
Ta = Value of T at commencement of liquid lead inward radial movement;
Tb = value of T when liquid lead reaches its maximum velocity within the gun barrel
Tc = value of T when liquid lead reaches the gun muzzle;
Td = value of T when liquid lead forms a closed spherical shell;
Te = value of T when fuel injection is complete;
Tf = value of T when random plasma is fully ionized;
Tg = value of T when Ep = (Ekld / 4);
Th = value of T when Ep = (Ekld / 2);
Ti = value of T when Ep = Ekld;
Tj = value of T when Ep = (Ekld / 2);
Tk = value of T when Ep = (Ekld / 4);

Ta = time at state a where Tc > Tb > Ta
Tb = time at state b where Tc > Tb > Ta
Tc = time at state c where Tc > Tb > Ta

Ta = time at start of spheromak formation (rely on context)
Tb = time at end of spheromak formation (rely on context)
Tc = time at spontaneous spheromak randomization (rely on context)

Ts = spheromak lifetime
Tsa = uncompressed spheromak life time
Tsb = compressed spheromak life time
U = field energy density
Uc = field energy density at R = Rc
Ue = (Epsilon / 2) E^2 = electric field energy density
Ueps = electric field energy density outside plasma sheet at (Rs, 0)
Uetc = electric field energy density inside plasma sheet at (Rc, 0)
Um = (1 / 2 Mu) B^2 = magnetic field energy density
Ump = poloidal magnetic field energy density outside the plasma sheet
Umpc = poloidal magnetic field energy density in spheromak core at (Rc, 0)
Umps = poloidal magnetic field energy density outside plasma sheet at (Rs, 0)
Uo = field energy density at (0,0)
Ur = cylindrical energy density
Us = spherical energy density
Vd = deuterium ion velocity in neutral plasma
Vda = deuterium ion velocity at state "a"
Vdb = deuterium ion velocity at state "b"
Ve = free electron axial velocity in plasma hose
Vea = free electron velocity at time T = Ta
Veb = free electron velocity at time T = Tb
Vep = free electron velocity component contributing to poloidal magnetic field
Vet = free electron velocity component contributing to toroidal magnetic field
Vex = free electron velocity in x direction in neutral random plasma
Vey = free electron velocity in y direction in neutral random plasma
Vez = free electron velocity in z direction in neutral random plasma
Vi = ion axial velocity in plasma hose
Vip = ion velocity component contributing to poloidal magnetic field
Vit = ion velocity component contributing to toroidal magnetic field
Vix = ion velocity in x direction in neutral random plasma
Viy = ion velocity in y direction in neutral random plasma
Vit = ion thermal velocity
Viz = ion velocity in z direction in neutral random plasma
Vl = velocity of liquid lead wall
Vla = 300 m / s = value of Vl at start of random plasma compression
Vlb = value of Vl at fusion ignition
Vol = neutral plasma volume
Voll = volume of liquid lead in compression sphere
Volv = volume of vacuum chamber
Vt = tritium ion velocity in neutral random plasma
Vtw = maximum tritium ion velocity impacting liquid lead wall
Vx = particle velocity in X direction
Vy = particle velocity in Y direction
Vz = particle velocity in Z direction
Xh = distance along plasma hose
Xp = distance along plasma hose in the poloidal direction
Xt = distance along plasma hose in the toroidal direction
Z = integration substitution variable (rely on context)

This web page last updated March 2, 2015