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THE
COLD CATHODE ARC
By
R.
H.
EATHER*
[Manuscript received
April
5, 1962]
Summary
Many
theories
have
been
proposed
in
the
last
15
years
to
explain
the
observed
high
current
densities
associated
with
the
cold
cathode
arcs.
All
of
these
theories
are
somewhat
inadequate
in
themselves,
but
a
combination
of
some
of
the
more
recent
theories
gives
a
satisfactory
explanation
of
these
high
current
densities.
I.
INTRODUCTION
The
term
" cold cathode
arcs"
is used
to
refer
to
those arcs
in
which
the
cathode spot
temperature
does
not
exceed say
2000-3000
°C.
They
are
the
arcs of
the
low boiling-point metals such as iron, copper, mercury. The high
current densities
at
the
cathodes of such arcs
cannot
be
explained
in
terms
of
simple thermionic emission. (These current densities are of
the
order of
10
5
-10
6
A/cm
2
.)
Several mechanisms
have
been suggested
in
the
past
15
years
to
explain
these high current densities. Some earlier theories were developed
to
account
for current densities of
10
3
A/cm
2
and
hence do
not
apply
to
the
current densities
now known
to
exist
at
cold cathodes. (For a review of earlier theories, see
von Engel
and
Robson (1957)
and
Llewellyn Jones (1953).)
II.
DISCUSSION
The modern theories,
in
brief, are as follows:
(i)
Perhaps
the
most
widely held view of
the
cold cathode arc mechanism
is
that
the
major
part
of
the
cathode current is carried
by
electrons
extracted
from
the
cathode
by
field emission,
the
high fields required being produced
by
the
space charge of positive ions
in
the
cathode fall space. Fields of
the
order
of
10
6
-10
7
V/cm account for
the
observed
current
densities. The threshold
potential
that
keeps
the
electrons
in
the
metal
is lowered
by
this strong electric
field, which permits
them
to
escape from
the
metal
in
great
numbers.
As
the
cathode fall is of
the
order of
10
V,
it
would
have
to
extend over
10-
5
-10-
6
cm
to
produce
the
high fields for field emission. Smith's (1946) experi-
ments on
the
thickness of
the
cathode
dark
space of
the
mercury arc (which is a
cold cathode arc) show
that
field emission cannot account for
the
observed
current densities
in
the
mercury arc. Loeb (1939) also shows
that
field emission
cannot account
by
many
orders of magnitude for
the
high
current
densities
observed
in
metal
arcs.
*
Physics
Department,
Newcastle
University
College,
Tighes
Hill,
N.S.W.;
present
address:
Antarctic
Division,
Department
of
External
Affairs,
Melbourne.
290
R.H.EATHER
(ii) A
new
theory
suggested
by
Rothstein
(1948) is applicable
to
arcs
with
low
spot
temperatures
and
relatively
high
spot
mobilities,
such
as
copper
and
iron.
It
is
assumed
that
a region possibly
10-
5
cm
thick
of
very
dense
metallic
vapour
exists
immediately
adjacent
to
the
cathode
spot. This
high
density
perturbs
the
atomic
fields so
that
the
normally
sharp
energy
levels
are
spread
into
bands,
including
conduction
bands.
Metallic
conduction
is
then
possible
from
the
cathode
to
this
region,
which
is
at
a
temperature
high
enough
to
emit
thermionically
into
the
plasma.
The
ions
bombarding
the
cathode
serve
to
maintain
the
high
local
density.
This
theory
is
supported
by
Smith's
(1946)
observation
that
a
continuous
spectrum
originates
within
10-
3
cm
of
the
electrode
surface.
Richardson's
equation
for
thermionic
emission is
jc=AT~
exp
(-<D/kTJ,
where
jc is
the
cathode
current
density
and
Tc
the
cathode
hot-spot
temperature.
<D
is
the
work
function
of
the
metal,
A a
constant,
and
k
the
Boltzmann
constant.
Tc is
given
by
Cobine (1941)
as
2400
oK
for
the
iron
arc, so
substitution
gives
jc~10-1
A/cm
2
which
is obviously
far
too
low.
Applying
Rothstein's
theory,
Tc becomes Tv,
the
temperature
of
the
dense
iron
vapour.
Assuming
that
this
dense
vapour
in
the
arc
plasma
is
at
the
same
temperature
as
the
plasma
itself
and
using Hefferlin's (1959)
value
of 4450 oK
for Tv for
the
iron
arc,
substitution
then
gives
jc~104
A/cm
2
•
Again
the
theory
does
not
explain
the
observed
cathode
current
densities.
(iii)
Another
theory
was suggested
by
von
Engel
and
Robson
(1957).
They
suggested
that
electrons
are
released
from
the
cathode
by
the
impact
of
excited
atoms.
The
electrons
gain
energy
in
the
cathode
fall
and
produce
excited
atoms
in
the
dense
vapour.
The
radiation
from
the
excited
atoms
diffuses
out
and
by
successive
absorption
and
re-emission
in
the
vapour
is
ultimately
absorbed
by
atoms
which
strike
the
cathode.
Positive
ions
are
formed
in
the
vapour
by
collisions
between
excited
atoms
and
by
electrons colliding
with
excited
atoms.
The
space charge of
the
positive
ions supplies
energy
for
evaporation
and
transfers
momentum
to
the
evaporated
atoms.
The
latter
effect
sets
up
a
vapour
density
close
to
the
cathode
which
is
many
orders of
magnitude
greater
than
elsewhere.
von
Engel
shows
that
the
process of
electron
emission
by
excited
atoms
whose
energy
does
not
greatly
exceed
the
work
function
is
very
efficient,
and
his
theory
accounts
for
the
high
current
density
of
the
mercury
arc.
The
mercury
arc
is
the
best
example
of
the
proposed
mechanism
as all
the
excited
states
of
the
mercury
atom
have
energies
greater
than
the
work
function
of
the
metal,
and
hence
are
capable
of releasing electrons.
For
iron
and
copper
cathodes,
however,
where
a
large
proportion
of
the
excited
states
have
excitation
energies
lower
than
the
work
function,
the
efficiency of
the
process is
greatly
reduced.
Note,
however,
that
von
Engel
has
given
a
mechanism
explaining
a
high
vapour
density
near
the
cathode
spot. This
was
previously
assumed
by
Rothstein.
THE
COLD
CATHODE
ARC
291
(iv) A
new
contribution
was
made
by
Cassie (1958).
He
suggested
that
in
the
pinch
effect
in
a
plasma,
the
inward
radial
force is
balanced
by
an
increase
in
gas
pressure
which is
unbalanced
axially.
The
plasma
maintains
its
state
of
electrical
neutrality
under
the
pinch
forces.
If,
however,
the
situation
in
the
metal
is considered,
the
fact
that
the
positive
charge
centres,
that
is,
the
crystal
lattice
points,
are
not
free
to
move
means
that
the
pinch
effect forces
are
not
balanced
by
an
electron
gas
pressure
but
only
by
space
charge
forces.
Thus
the
pinch
effect
sets
up
negative
space
charge
in
the
region of
high
current
density
near
the
cathode
spot.
The
effect of
this
negative
space
charge
is
to
lower
the
effective
work
function
<I>
by
~<I>.
Hence
the
Richardson
equation
becomes:
jc=AT~
exp
[-(<I>-~<I»/kTcl,
where
~<I>
is
given
by
~<I>""'fLEJA2
exp
[~(W
+<I>-~<I»]',
where
fL
and
E
have
their
usual
meanings, J is
the
current
density,
A is
the
slowing
down
length,
and
W is
the
Fermi
energy.
~<I>
has
the
value
of
2-3
V for
copper
and
1·5-2·5
V for
iron
(see Cassie 1958).
Substituting
for
the
case of
iron
and
using
Cobine's
value
of 2400 oK
for
Tc gives
jc~1'4
x10
2
to
1·7
x10
4
AJcm
2
•
Again
the
theory
does
not
explain
the
observed
current
densities.
However,
if
theories (ii), (iii),
and
(iv),
each
of
which
is
somewhat
inadequate
in
itself,
are
combined,
then
a
reasonable
explanation
of cold
cathode
emission
is
obtained.
von
Engel
and
Robson's
theory
gives a
mechanism
explaining
a
high
vapour
density
near
the
cathode
spot.
Applying
Rothstein's
theory
to
this
high
density
vapour
accounts
for
current
densities of
the
order
of
10
4
A/cm
2
(for
the
iron
arc).
Now
if
the
pinch
effect which
results
in
a lowering of
the
work
function
is also
considered (as
in
Cassie's
theory),
the
Richardson
equation
becomes
jc
=AT~
exp
[
-(<I>
-~<I»/kTv]'
Substitution
for
iron
now
givesjc~5
x 10
5
-5
X10
6
A/cm
2
,
which is of
the
observed
order.
Similar
calculations for
copper
give a jc
ranging
from
2·5
x10
6
to
7·5
x10
7
A/cm
2
,
depending
on
the
value
of
~<I>
chosen
and
on
the
value
of Tv
used
(values of Tv
quoted
in
the
recent
literature
vary
from
4500-6100 °C).
Thus
the
combined
theories
predict
the
observed
current
densities.
The
calculated
current
densities
are
very
dependent
on
the
value
of
~<I>
used,
and
more
accurate
values
of
~<I>
must
be
determined
before
any
certainty
can
be
placed
on
the
validity
of
the
calculated
current
densities.
III.
REFERENCES
CASSIE,
A.
M.
(1958).-The
arc
cathode.
Nature
181:
476.
COBINE,
J.
D.
(1941).-"
Gaseous
Conductors."
(McGraw·Hill:
New
York.)
VON
ENGEL,
A.,
and
ROBSON,
A.
E.
(1957).-The
excitation
theory
of
arcs
with
evaporating
cathodes.
Proc.
Roy.
Soc. A
243:
217-36.
292
R.H.EATHER
HEFFERLIN,
R.
(1959).-Behavior
of
the
d.c.
iron
arc
and
its
usefulness
in
the
determination
of
f
values.
J.
Opt. Soc.
Amer.
49:
680-4.
LLEWELLYN
JONES,
F.
(1953).-Electrical
discharges.
Rep.
Progr. Phy8.
16:
216-65.
LOEB,
L.
B.
(1939).-"
Fundamental
Processes
of
Electrical
Discharges
in
Gases."
(Wiley:
New
York.)
ROTHSTEIN,
J.
(1948).-On
the
mechanism
of
electron
emission
at
the
cathode
spot
of
an
arc.
Phy8. Rev.
73:
1214.
SMITH,
C. G.
(1946).--Cathode
dark
space
and
negative
glow
of
8
mercury
arc.
Phy8. Rev.
69:
96-100.