Formation processes and secondary emission coefficients for H/sup -/ production on alkali-coated surfaces Page: 4 of 7
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? = r + z,
n = r - z,
4> = <J>.
Upon setting the azimuthal quantum number equal to
zero, expressing lengths and energies in units of
Bohr radii and Rydbergs, respectively, and des-
cribing the negative ion by a coulomb state with
effective charge Z and unperturbed energy level
equal to Z2, the introduction of coordinates (5)
into eq. (1) leads to an n equation
The term V0 in the brackets is a uniform potential
within the substrate; the term VI is a constant
term equal to the surface work function and
applicable in certain regions (see figs. 3 and 5);
the next two terms arise from the coulomb term
and coordinate choice, respectively; the term with
electric field coefficient occurs in those
regions of uniform electric field; the last term
in the brackets is the image term, with zQ the
z-coordinate of the imqe plane measured from the
center of the negative ion. The separation of
coordinates fails only in the case of the image
term which contains the c coordinate explicitly.
As Janev was the first to point out, £ « n in
the range of integration, and by neglecting this
coordinate in the image term we have effectively
achieved a separation.
The function v(n) is complex. Writing
v = u + iw and introducing into equation (6), we
obtain a pair of coupled equations for the real
and imaginary functions of v ;
■f(£ + VI+T*7+-n'
■1|E + VI + 1,Z' +Vfcn‘
n + ?z0
We are interested in a solution of Eqs. (7) which
represents a standing wave negative ion function
in the negative ion region and a purely outgoing
wave propagating in the region of the wefa? sub-
strate. Referring to Eq. (6), within the sub-
strate this equation reduces to
Equation (9) has the form required for a purely
outgoing wave. Matching this solution to the
interior solutions for u and w at the boundary of
the substrate, the matching conditions become
u*u + w*w
Uz + wz
uw1 - wu*
ip) *>l p)! * «f
The integration procedure consists of select-
ing a negative ion separation distance Zp, and
searching for values of E and r which satisfy the
conditions (10), The resulting value for r gives
the transition rate, r/TT, at that separation
distance. The rate of loss of electron density
is, from (4),
=. i m2
dt tr m •
the loss rate T/Tf is a function of separation
distance z0; writing dt = dz0/v, where v is the H”
ion velocity as it moves away from the surface,
the fraction of H~ ions surviving the electron
loss to the substrate becomes
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Hiskes, J.R. & Karo, A. Formation processes and secondary emission coefficients for H/sup -/ production on alkali-coated surfaces, article, September 20, 1977; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc1074337/m1/4/: accessed November 14, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.