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From YouTube: The Inverted Plasma Sheath, Grant Johnson
Description
When an electron emitting surface is in contact with a collisional plasma, a unique regime of plasma sheath may form, an inverse sheath. The inverse sheath regime most notably differs from the classical Debye sheath by having a floating potential above that of the plasma potential. This leads to a restructuring of the plasma flows. The ubiquity of emitting surfaces in laboratory plasmas means there are a number of applications of the inverse sheath such as extending hot cathode lifetimes, cooling of the local plasma, and modifications to emissive probe theory. Due to the collisional nature of the sheath and the trapped population of ions, kinetic simulations are required to answer outstanding questions which remain about the sheath’s formation, and transport properties. To address these questions, we have developed 1D-1V and 2D-2V kinetic continuum codes which include collisions and allows us to explore the inverse sheath in relevant configurations. In this talk I will introduce the fundamentals of the inverse sheath, the codes we have developed to solve these problems, and the applications of the inverse sheath.
A
A
We
started
these
series
of
awards
to
try
to
recognize
some
of
the
outstanding
work
that
is
done
by
Young
researchers
using
nerveskin
and
given
an
opportunity
to
share
and
to
recognize
what
they've
done.
Today
we
have
Grant
Johnson
from
Christian
University
and
at
Livermore,
National
Lab
I
believe
he
did
his
undergraduate
work
that
was
nominated
while
working
in
conjunction
with
Livermore
as
well,
so
welcome
Grant,
and
we
have
one
thing
to
share
with
you,
which
is
a
certificate
recognizing
your
achievement
for
helping
elucidate
previously
unexplained
plasma,
surface
interactions
in
Tokamak,
Fusion
Energy
reactors.
A
B
C
Actually,
okay,
so
the
inverted
plasma
sheath,
so
my
name
is
Grant
Johnson
I
did
this
work
was
an
undergraduate
at
Embry,
Riddle,
Aeronautical,
University
and
I
have
now
moved
to
Princeton
University
as
a
graduate
student
in
the
plasma
program.
This
was
done
in
collaboration
with
Michael
campanelle.
C
C
So
I'm
going
to
talk
with
talk
through
the
different
electrostatic
sheath
regimes
that
you
can
get
their
initial
Discovery
and
the
properties
of
the
inverse
sheath,
the
computational
model
that
we
ended
up
using
the
simulations
and
results
that
we
have
so
to
start
with
electrostatic
sheaths,
so
the
classical
Like
Chief,
discovered
by
langmir
is
called
in.
This
paper
is
a
classical
or
the
stock,
the
classical
chief.
So
it's
also
been
called
other
things,
such
as
a
device
sheath.
C
But
what
you
end
up
having
in
this
plot,
we
have
the
potential
versus
the
distance
from
the
surface
normalized
to
the
Dubai
length
is
the
four
different
types
of
sheaths
that
you
can
possibly
have.
The
first
is
the
classical
light
sheath,
where
you
have
no
emission,
you
have
a
boundary
located
at
x,
equals
zero
and
you
have
the
plasma
potential
set
at
a
far
away
distance,
much
farther
than
the
range
of
this
plot
to
be
V
of
zero
Phi
of
zero.
C
These
this
can
be
achieved
by
a
thermionic
emission
or
for
the
scl
marginal
SEO
things
like
secondary
electron
emission.
So
what's
the
difference
between
these
different
things,
why
are
they
all
on
the
same
plot?
So
the
marginal
scl
case
is
right.
When
the
wall
potential
starts
to
change,
you're,
no
longer
repelling
electrons
and
keeping
them
to
the
bulk
plasma
and
accelerating
ions
to
the
surface
as
strongly
as
you
were
before,
and
the
reason
for
the
decrease
in
potential
is
that
the
electrons
are
now
being
emitted
from
the
surface
itself.
C
If
you
keep
increasing
the
knob
on
the
amount
of
emission
you
can
get,
you
can
get
an
scl,
sheath
and
given
collisions
in
enough
time.
The
potential
minimum
here
in
the
green
line,
otherwise
known
as
the
virtual
cathode,
can
accumulate
positive
charges
and
form
an
inverse
sheath.
The
I've
lost
my
cursor,
the
blue
line
here.
C
So
what's
the
difference
between
these
different
sheets?
So
first
you
have
the
floating
case.
What
we
considered
on
this
plot
to
the
left
is
that
the
surface
is
allowed
to
take
whatever
potential
is
required
of
it
in
order
to
maintain
a
net
current
of
zero
and
the
steady
state
and
the
surface
electron
emission
is
present
in
these
ladder.
Three.
C
Of
course,
so
we
consider
a
one-dimensional
code,
so
it's
1D
One
V.
So
we
have
one
velocity
Dimension,
because
it's
electrostatic,
that's
all
we
need
the
there's.
A
wall
located
at
x
equals
zero
and
far
away
at
about
100
to
200
x
over
Lambda
to
buy.
We
have
a
symmetry
plane
and
this
wall
is
allowed
to
take
whatever
potential
relative
to
the
plasma
that
it
wants
to.
Okay,.
C
C
C
C
So
it's
the
same
as
the
potential
you
end
up
getting
charge
separation
and
then
that
positive
layer
near
the
surface,
the
electrons
are
suppressed
by
the
red
potential,
because
this
is
the
classical
potential
while
the
ions
are
accelerated
into
the
wall
and
the
scl
sheath,
the
acceleration
is
not
as
great,
although
the
ion
profile
looks
very
similar.
You
end
up
getting
an
electron
growth
near
the
surface,
and
this
is
because
you
have
electrons
being
emitted
from
it.
C
Now
the
real
difference
is
once
you
start
having
emitted.
Electrons
are
like
you
start
having
mid
electrons
in
the
scl
case,
but
once
you
allow
time
for
collisions
to
accumulate
ions
positive
charges
in
this
scl
potential.
Well,
you
can
accumulate
a
significant
growth
of
them
near
the
surface,
and
these
ions
end
up
collapsing.
This
negative
charge
region
and
you're
ending
our
positive
charge
region.
Sorry
from
about
X
of
one
to
X
about
7.5
you're,
just
left
with
a
negative
charge
very
close
to
the
wall.
C
This
is
truncated
in
the
density,
because,
if
not,
this
density
of
electrons
can
be
huge
compared
to
the
plasma
density
in
order
to
achieve
an
inverse
sheath.
But
typically,
your
density
is
rather
low
compared
to
this
and
you're.
The
reason
you
need
this
is
because
you
have
a
large
separation
and
your
emitted
electron
temperature
over
your
plasma,
electron
temperature
all
right.
So
where
was
this
first
scene?
So
this
is
Discovery
part
one,
the
experiments
originally,
if
you
have
a
glow
discharge,
so
this
is
results
from
Greiner
at
all.
C
It's
PRL
of
1993.,
the
cathode
sheath,
which
is
located
at
x,
equals
zero
here
between
an
Electro
and
sorry,
a
cathode
is
located
at
x,
equals
zero,
an
antanode
located
at
X
of
150
millimeters.
You
end
up
with
most
of
the
potentials
taken
over
the
cathode
sheath.
So
if
you
had
anything
in
this
region,
it
would
get
accelerated
for
electrons
out
towards
the
other.
C
Or
ions
it
would
be
absorbed
into
the
surface.
Now,
if
you
end
up
with
a
significant
amount
of
surface
emission,
which
is
the
difference
between
this
panel,
a
and
panel
B
potential
versus
position,
plots
grinder
noticed
that
you
could
end
up
forming
a
plasma
potential.
That's
at
the
cathode
or
near
the
cathode
potential,
so
trying
to
explain
this.
C
He
followed
it
up
with
simulation,
so
these
simulations
show
the
potential
structure
versus
the
plasma
potential.
With
the
Catholic
potential
marked
with
this
dotted
line,
you
notice,
there's
a
small
potential
drop
in
the
plasma
potential
everywhere
is
below
the
wall
potential
and
you
then
have
a
rise
on
your
anode
G,
so
electrons
are
being
emitted
from
the
left
surface.
C
They
diffuse
through
this
middle
region
and
then
they're
accelerating
out
to
the
right
surface,
and
this
acceleration
is
enough
to
excite
neutrals
and
you
end
up
getting
a
glow
in
that
region,
which
is
why
they
call
it
the
anode
glow
mode.
Typically,
when
you
have
this
and
another
way
to
look
at
this
is
to
look
at
the
density
plots
and
you
can
see
you
end
up
with
electron
Rich
region
near
the
surface
and
an
ion
polar
region
and
you
have
ions
can
find
primarily
to
this
bulk
potential
flat
potential
region.
C
So
another
way
to
look
at
this
and
we'll
look
at
this
quite
frequently
in
a
phase
space
picture
of
the
Velocity
as
a
function
of
X
over
here.
They
normalize
it
to
10
to
6
meters,
but
anything
was
positive.
A
velocity
for
the
electrons
are
moving
to
the
right
and
negative
is
moving
to
the
left.
Well,
the
ions
you
can
see
are
tracked
in
the
region
of
face
space
and
they
can't
make
it
to
either
boundary.
C
So
this
was
a
1D
pick
simulation
by
Griner,
followed
two
years
after
he
did
his
initial
experiments
to
explain
what
he
observed
and
another
person
came
along
Michael
campanell,
who
started
to
look
at
what
if
he
had
two
surfaces
that
have
strong
emission
here,
he's
looking
at
secondary
electron
emission
from
each
surface
and
notice
that
you
can
actually
Force
the
plasma
everywhere
to
be
below
the
potential
of
the
surfaces.
So
this
is
also
a
1D
pick
code.
C
All
right.
So
an
overview
of
what
we
just
talked
about.
An
inverse
sheath
can
form
when
you
have
a
gamma,
which
is
what
we'll
be
using
quite
a
bit
of
greater
than
or
equal
to
about.
One
and
Gamma
here
is
defined
as
the
outgoing
emitted
electron
flux
over
the
incoming
plasma
electron
flux.
In
the
simulation,
the
plasma
potential
and
the
inverse
sheath
can
be
below
the
wall
potential.
C
It
can
be
below
both
the
cathode
like
in
the
bias
case
and
in
the
floating
case.
You
end
up
getting
a
positively
charged
surface.
There
is
no
net
current
in
the
steady
state
to
the
wall
for
the
floating,
but
there
is
in
the
bias
case,
and
then
what
we'll
show
in
a
minute
is
that
you
can
get
a
cooling
of
the
electrons
up
to
the
surface
excellent.
So
what's
the
1D
code,
the
1D
code
is
a
1D
1V,
kinetic
Continuum
electrostatic
code.
E
C
We
also
include
surface
electron
emission
in
this
code
and
we
it's
written
in
serial
IDL
and
we
use
an
Euler
step
in
time
and
space
and
various
initial
boundary
conditions.
So
this
is
the
first
step
in
the
simulation
story.
We
started
with
a
1D
code
and
eventually
we
are
going
to
go
to
a
2d
code,
but
to
really
understand
what
we're
doing
and
why
we
did
things
in
the
2D
code.
C
C
We
have
our
known
B
field,
and
this
we
have
spatial
infection
of
particles
to
move
in
space,
and
then
we
have
charge
Source
terms
which
are
created
uniformly
throughout
our
volume
here
and
1D
and
then
later
in
2D,
and
then
we
have
our
collisions,
which
can
be
any
of
the
ones
I
just
described.
This
is
coupled
with
a
poisson
equation
which
allows
us
to
get
our
potential,
so
results
of
1D
simulations.
This
is
our
part.
One,
the
first
question
Mike
and
Maxime
were
asking:
is
our
two
equilibrium
States
possible?
C
When
do
you
get
an
scl
versus?
When
do
you
get
an
inverse
sheath?
So
what
we're
looking
at
here
are
the
phase
diagrams
from
the
kinetic
Continuum
code,
the
First
Column
we're
looking
at
no
collisions
in
the
sheath
region
when
you
have
a
classical
sheath
formed
here.
So
the
same
plots
of
potential
intensity
we've
seen
before,
but
now
we're
looking
at
the
phase
profiles,
so
you
have
exponential
decay
of
the
density
of
electrons
towards
the
surface
and
you
have
acceleration
of
ions
towards
the
surface.
C
C
You
have
no
collisions
still
in
the
sheath
region
and
you
have
an
electron
beam,
which
is
this
red
higher
density
of
electrons,
coming
off
the
surface
and
being
accelerated
by
the
sheath's
potential,
while
the
ions
are
now
not
gaining
as
much
energy
as
they
were
before,
but
we're
not
seeing
this
transition
to
inverse
now.
The
critical
distinction
here
is
once
we
start,
including
collisions,
and
we
allow
for
enough
time
to
pacify
that
the
collisions
can
accumulate,
charge
and
invert
the
sheath.
C
This
is
approximately
equal
to
the
amount
of
charge,
disturbance
that
you
have
before
needs
to
be
neutralized
by
the
accumulated
charge,
and
we
use
that
in
a
minute
to
describe
about
how
long
this
transition
will
take
and
that's
important.
If
you
have
other
loss
sources,
you
need
to
to
make
sure
you're
dominating
the
transition
by
having
enough
collisions
and
accumulating
enough
charge
in
time,
if
not
you'll,
end
up
looking
like
a
potential
SCLC.
C
C
So
another
result
of
the
1D
simulations
are
from
my
campanelle
and
his
2018
pre.
You
have
the
cathode
and
anode
set
to
a
fixed
bias
between
them
and
you
end
up
getting
the
same
results
that
grinder
noticed
in
its
particle
on
cell
and
his
experimental
simulations.
So
we
verify
that
you
still
get
an
inverse
like
she's
near
the
surface
and
a
potential
minimum
in
our
simulations.
You
have
electron
trajectories,
like
I
just
traced
out
a
lot
of
them,
though,
are
suppressed
by
the
small
potential
drop
and
once
they,
if
the.
C
And
are
able
to
get
out
of
this
potential
drop
stream
across
this
neutral
region,
which
is
where
you
have
equal,
ions,
two
electrons,
and
then
they
enter
the
anode
sheath
and
are
accelerated
out
into
the
anode
plate,
which
is
located
at
the
right
hand
side
of
these
plots.
So
looking
at
density,
we
agree
with
the
same
density
profiles
that
they
get
and
then
for
finite
ion
temperature
effects.
You
can
end
up
introducing
gradients
caused
by
your.
C
You
have
a
now
just
a
different
density
caused
by
finite
ion
temperature,
so
these
need
to
offset
each
other
to
have
about
equal
plasma
pressure
at
all
points.
So
you
form
a
gradient
in
this
LP
region
here.
So
there's
a
number
of
modifications
that
were
looked
at
and
this
gradient
will
come
back
and
later
2D
simulations.
C
So
this
is
about
the
time
that
information
everything
we've
seen
before
was
known
once
I
joined
the
team
at
Livermore
and
one
of
the
things
that
we
started
with
for
the
1D
simulations
was
looking
at
what
happens
to
the
electron
temperature
near
the
surface.
So
what
I
have
here
is
electron
temperature
plots
versus
their
distance,
so
electron.
C
You
have
a
heating
region
for
electrons
upstream
and
you're,
asking
what
happens
for
the
different
types
of
sheaths
so
classical
like
for
blue
and
purple,
and
you
start
emitting
more
electrons
until
you
get
to
an
scl
like
for
green
and
then
eventually
an
inverse
like
for
the
Pink
So.
In
this
case,
we
showed
that
you
can
end
up
getting
lower
temperature
until
eventually
it's
lowered
in
the
inverse
sheath
to
match
the
target
temperature
the
T
emit
at
the
boundary.
C
So
this
could
be
an
important
consequence
to
achieve
diverter
Detachment
that
has
potential
applications
in
that
area
and
that's
something
that
Mike
campanell,
Alex,
frieden
and
Dave
groh
are
looking
at
with
warp
and
warp.
X
is
what
happens
in
more
tocamoc
relevant
configurations
when
you
have
like
an
oblique
B
field
as
well.
This
Cooling
and
potentially
reducing
the
high
end
environment
by
having
a
plasma
potential,
that's
lower
than
the
surface
potential
and
no
longer
accelerates
ions
into
the
surface,
could
extend
the
lifetime
of
devices
like
hot
cathens
all
right.
C
This
was
written
up
in
a
Peoria
in
2019
by
Mike
and
me
and
then
well
what
happens
if
these
particles
can
leak
out.
So
this
is
a
figure
from
Brian
cross
and
you
have
any
races
paper
from
2018
about
strongly
emitting
filament
that
potentially
could
form
an
inverse
sheath,
although
it's
they
explain
the
not
total
formation
of
it
in
Hershey's
and
more
of
an
scl
like
sheath,
by
diffusion
to
the
surface.
So
these
questions
are
definitely
important.
What
role
does
this
2D
surface
play
versus
a
planar
geometry?
C
It's
content,
Continuum
and
based
on
the
same
model
for
the
1d1b,
so
the
blue
is
the
highlighted
changes.
Originally,
this
was
written
in
IDL
to
sort
of
test
the
concept
and
make
sure
everything's
working
okay
and
then
it
was
extended
to
a
hybrid
openmp
MPI
code
and
see
so
this
is
where
nurse
started
playing
a
significant
role
in
how
to
actually
run
these
simulations.
C
C
C
So
one
thing
that
we
have
is
the
poisson
solve
I
wrote
this
myself.
The
reason
I
really
wanted
to
write
this
2D
code
myself
was
to
get
a
better
understanding
and
not
just
have
a
black
box
of
I
put
in
plasma
parameters
and
I
get
out
results.
I
I
really
have
been
interested
in
how
to
write
simulations
and
what's
required
to
build
them,
and
the
most
challenging
component
for
me
was
writing
an
efficient
hybrid
scheme
to
solve
poisson's
equation.
So
here,
I
use
multiple,
four-year
analysis.
C
The
results
aren't
efficient
are
not
efficient,
sorry
aren't
important,
but
how
we
paralyze
the
scheme
is
so
each
of
the
eigen
modes
are
calculated
on
different
CPUs,
so
each
CPU
is
connected
to
one
shared
memory
on
a
single
node,
and
then
we
can
sum
these
all
together
to
find
the
potential
surface
and
another
way
to
do.
This
is
to
also
break
up
our
memory.
We're
having
issues
where
you
know
we
upgrade
from
you
know:
One
desktop
to
nurse.
C
Can
we
have
a
lot
more
memory,
but
we
still
run
out
of
memory,
so
we
need
a
distributed
memory
model
and
we
connect
all
our
nodes
with
MPI
and
then
have
one
each
node
openmp,
pushing
our
particles
and
solving
the
poisson
equation.
So
MPI
is
used
to
hand
off
all
the
boundary
conditions
and
the
fluxes
at
each
of
the
boundaries,
while
the
each
of
the
nodes
do
the
heavy
lifting
on
CPUs
with
uniform
memory
access
foreign.
C
So
one
of
the
results
that
we
have
for
2D,
so
I'm
not
going
to
go
through
all
the
results,
because
there's
quite
a
few.
What
we
did
to
verify
our
2D
code
is
reproducing
what
we
expect
our
1D
results.
We
went
through
the
cases
that
we
saw,
such
as
floating
surfaces,
bias
surfaces,
and
we
saw
that
we
were
able
to
do
things
like
reproduce
the
2D
anode
Global
that
we
saw
in
one
key
and
showed
that
there
are
emitting
surfaces
that
can
still
have
ion
trapping.
C
So
this
is
the
results
just
to
get
a
bearing
first
of
how
we
extended
the
anode
glow
mode
from
a
1D
case
into
a
2d
case,
I'm
going
to
go
through
this
kind
of
slowly
just
to
understand
what
these.
All
these
plots
are
so
we
have
the
distance
from
the
center
and
Y
and
we
have
the
distance
from
the
center
in
X.
We
still
have
our
absorbing
boundaries.
This
is
our
case.
Two
configuration
with
a
beige
electrode
located
near
this
bottom
left
corner.
C
Ion
density
plotted
as
a
maximum
of
the
density
to
zero,
so
the
higher
or
the
darker,
the
color,
the
higher
the
density
well
for
electrons
you'll
end
up
with
a
similar
plot.
But
now
we've
cut
off
just
a
slight
region
near
the
surface
because
we
have
so
much
surface
emission.
You
end
up
overwhelming
your
Contour
plot.
If
you
don't
cut
it
off
at
some
point,
so
these
two
plots
are
showing
the
true
2D
nature.
C
We
still
have
the
pressure
balance
in
this
case
and
that's
causing
this
Decay
one
over
R
like
decay
of
the
density
moving
away,
and
you
still
form
this
quasi-neutral
region,
although
it
doesn't
look
quite
the
same
and
you
still
have
an
inverse
she's
forming
along
the
inner
electrode
and
on
along
the
outer
electrode.
You
have
this
anode
sheath
that
picks
up
most
of
the
plasma
potential.
C
C
Our
same
current
that
submitted
so
this
scl
electron
current
density
limit
is
shared
in
planar
geometry.
So
what
we're
plotting
here
is
the
current
density
versus
the
simulation
time
and
the
valves
that
we're
controlling
on
this
is
the
amount
of
emitted
electron
flux
over
time.
So
we
keep
notching
it
up
to
see
all
right
well
in
2D,
if
it
behaves
like
1D,
you
would
expect
this
green
line
and
then
our
blue
line
for
the
net
electron
current
density
to
be
identical.
C
C
C
Your
ions
don't
play
much
of
a
role,
so
it's
really
a
balance
between
your
electrons
and
the
amount
of
charge.
You
can
accumulate
in
the
sheath,
so
this
is
used
to
understand
the
next
plot,
so
this
current
enhancement
over
the
space
charge,
limited
sheath,
will
give
us
a
hint
at
what's
going
on
when
we
compare
IV
probe
traces.
C
C
So
the
best
way
to
see
what
plasma
like
a
very
large
plasma
is
a
very
small
probe
would
look
like
it
actually
takes
the
difference
between
these
two
and
what
we
end
up
seeing
is
that
in
the
classical
Lake
sheath
we
get
our
standard,
IV
probe
trash.
You
have
a
ion
saturation
limit
and
when
you
have
a
strong
negative
potential
and
you
have
an
electron
saturation
limit
and
you're
positive
region
of
V
probe
over
the
plasma
potential.
B
C
10.
in
the
first
region,
between
about
minus
45
volts
and
about
minus
25
volts,
you
still
form
a
classical
like
sheath.
Your
potential
is
too
great
and
you
still
take
up
your
most
of
your
potential
drop
over
the
cathode
Chief.
So
all
of
the
electrons
that
are
emitted
are
able
to
get
out
and
that's
why
you
have
this
huge
discrepancy
in
the
current
density
between
your
not
emitting
probe
and
your
emitting
probe
once
you
start
sweeping
that
upwards
and
you
have
collisions
something
new
occurs
that
was
not
seen
before.
C
C
You
end
up
with
a
very
steep
new
region
of
your
IV
Trace,
and
you
end
up
going
into
your
electron
saturation
here
so
where
the
plasma
potential
is
where
your
probe
is
equal
to
your
plasma
potential
can
be
located
at
the
intercepts
here,
and
the
difference
between
prior
studies
in
this
study
is
that
you
end
up
getting
about
10,
more
volts
potential
difference
between
you're,
not
emitting,
and
your
emitting
case.
So
this
is
a
significant
difference.
C
If
you're
trying
to
carefully
measure
your
plasma
within
emissive
probe,
this
will
be
some
an
effect
that
you
have
to
be
aware
of.
If
you
have
a
very,
very
low
density
plasma,
so
the
virtual
cathode
itself
is
located
with
VC,
and
this
is
when
the
potential
well
starts
forming.
So
that's
what
the
VC
forming
is
here.
C
Another
way
to
look
at
this
and
see
is
a
VC
formation,
as
well
as
the
classical
sheath
is
to
look
at
profiles
of
the
potential.
So
this
is
again
at
y,
equals
zero,
we're
taking
from
our
electrode
to
our
anode
at
the
right,
our
potential
profile
and
we're
seeing
that
as
we
reduce
the
potential
you
can
start
forming.
This
virtual
cathode
ions
are
accumulating
and
allowing
out
more
current,
which
explains
our
steeper
our
iron
current
density
being
more
negative,
and
eventually
you
end
up
forming
an
inverse
sheath
near
the
submitting
surface.
C
Once
you
have
a
high
enough
bias,
this
inverse
sheath
potential
will
keep
growing
relative
to
the
plasma
potential
to
suppress
farther
emission,
and
that's
why
you
end
up
getting
this
short
tail
on
the
electron
saturation
part
of
the
probe
sweep
all
right.
The
final
part
that
we
have
is
hysteresis.
So
how
would
we
determine
if
we
had
an
emissive
probe
in
a
plasma?
C
C
So
if
you
start
at
minus
30
volts
with
the
same
configuration
that
we
were
showing
before
so
this
is
a
pro
potential
versus
time
and
you
pulse
it
up
to
20
volts
you're,
now
pulsing
between
classical
like
sheath
and
inverse
sheath,
if
he
pulls
back,
you've
now
formed
this
inverse
sheath
and
you've
restructured
ions
and
everything
near
the
surface,
you're
going
to
expect
a
hysteresis
as
well
as
different
currents
during
different
times
of
your
pulse.
So
one
way
to
look
at
this
is
the
current
density
versus
the
probe
potential.
C
As
you
start
out
at
large
negative
biases,
you
allow
all
your
current
density
and
then
once
you
pulse
as
a
probe
to
an
inverse
sheath,
you've
suppress
most
of
that
if
you're
around
the
potential
of
the
plasma
you'll
be
about
zero
volts.
So
this
is
your
condition
for
your
floating
case.
You'll
end
up
with
zero
current,
so
you
can
imagine
how
that
would
occur
if
you
went
too
high
above
your
plasma
potential,
you
end
up
with
the
opposite
occurring
and
your
probes
absorbing
your
plasma
electrons.
C
In
that
case,
you
end
up
with
a
very
negative
current
density.
Another
way
to
look
at
this
is
the
current
density
versus
time.
So
if
we
focus
on
just
around
the
pulse
region,
you
end
up
with
your
strong
current
density,
and
then
you
pulse
it
to
near
the
plasma
potential
and
you're
able
to
see
the
flat
top
here
from
about
being
in
the
floating
condition.
C
So
what
we
end
up
getting
from
this
is
that
you
can
pulse
the
different
sheath
regimes
and
I
have
more
slides
if
people
are
interested
and
the
backup
slide
portion
for
looking
at
pulsing
between
different
sheaths
but
you're
able
to
determine
where
the
floating
potential
is,
as
well
as
where
the
she's
around
the
probe
is
inverted
scl
or
classical.
Like.
C
Oh
sorry,
and
one
other
way
to
look
at
this
sorry
is
to
end
up
cycling
through
one
to
four.
So
you
can
see
what
I
traced
out
before
is
cycling
from
point
one
to
point
two
to
three
to
four
and
it's
the
same
thing
as
far
as
the
current
density,
so
the
future
experiments
and
directions
that
we
hope
to
take
this
in
I
couldn't
help
but
throw
in
future
directions
for
the
theory
too
apologize.
C
C
C
Dielectric
surfaces
are
something
that
are
interesting
to
extend
the
2d2v
code
and
there's
currently
not
a
adequate
understanding
of
what
a
self-spike
instability
that
we
see.
I
haven't
really
presented
that
here,
but
you
can
end
up
exciting
modes
that
are
not
identified
at
the
moment,
but
hopefully
can
be
described
in
the
future.
So
the
experiments
that
are
currently
in
the
works
are
at
UCLA,
looking
at
the
large
plasma
device
and
electron
Cooling
and
then
there's
a
pppl
emissive
probe
experiment
with
Jeff
getting
rates
and
Mike
campanelle.
C
C
C
C
I
wrote
a
different
code
for
successive
over
relaxation
to
find
the
potential
in
the
odd
geometry
cases
that
we
became
more
interested
in
so
now
you
can
have
arbitrary
boundaries
located
pretty
much
anywhere
in
your
plasma
with
a
new
solver.
The
hope
is
eventually
to
couple
the
code
to
something
like
a
linear,
algebra,
solver
pack,
a
hyper
and
that
that's
kind
of
a
future
direction.
For
this,
the
2D
to
be
kinetic
Continuum
code.
A
Yeah
thanks
great
great
today's
biggest
question
is
raise
your
hand
or
type
me
to
chat.
I
have
a
bunch
of
questions,
I'm
sure
I
won't
get
through
them
all,
but
no
I'm,
not
an
expert
in
this
field,
of
course,
but
on
your
simulations
they're
time
dependent
simulations.
But
do
you
do
you
reach
a
steady
state
eventually,
or
is
this
a
situation,
a
dynamic
situation
that
the
conditions
are
always
changing
in
some
way
and
then
what
what
was
the
kind
of
initial
configuration
initial
State?
We
started
from.
C
C
So
we
start
with
a
Maxwell
line
distribution
and
allow
that
to
evolve
to
a
steady
state
and
then
later
we'd
introduced
a
mission
in
some
cases.
In
some
cases,
we'd
start
with
a
mission.
It's
a
large
range
of
different
things,
but
typically
we'd
want
to
evolve
either
to
a
case
where
we
have
no
emission
we'd
get
classical
like
sheaths
on
all
surfaces,
or
we
would
want
to
move
to
a
case
where
we
started
with
a
mission
and
we
go
forward.
C
A
C
So
we
can
go
back
inside
I
when
I
came
to
Livermore
I
had
one
introduction
to
coding
in
Matlab,
and
that
was
it.
This
was
my
sophomore
year,
I
think
Mike
campanellport,
not
holding
that
against
me
and
I
came
in
and
I
learned
to
see
an
open
MPI
through
both
and
IDL
through
Mike
avidel,
Maxim,
umanski
and
Blaze
Barney
also
held
for
an
introduction
to
openmp
and
MPI
workshop
at
Livermore.
C
A
Yeah
excellent
well,
that
was
a
that
was
a
lot
to
learn.
Then
that's
great
that
you
did,
that
did
you.
How
did
you
think
the
code
performed?
Did
you?
Did
it
run
as
quickly
as
you
would
have
expected,
based
on
your
kind
of
Serial
experiences,
and
did
you
ever
look
at
any
kind
of
performance,
metrics.
C
We
we
did
look
at
some
very
basic
performance
metrics
as
far
as
like
particles
pushed
per
second
per
node.
The
number
was
about
eight
billion
particles
per
node
pushed
per
second,
but
you
know
benchmarking
that,
to
other
things,
hasn't
really
been
done.
So
it's
hard
to
kind
of
you
know
give
a
fiduciary
of
where
that's
at
compared
to
other
codes,
but
compared
to
our
serial
code.
If
we
gave
it
say
eight
nodes
versus
a
Serial
couple.
It's
it's
hard.
C
It's
difficult
to
compare
in
that
case,
because
you
have
a
lot
more
memory.
We
didn't
really
compare
the
same
memory
of
one
to
another,
but
we
were
getting
very
good
scaling
in
the
poisson
solver.
That
was
our
typical
bottleneck
that
we
had
and
the
next
was
the
charge.
Advection
and
I
see
a
question
from
Alex
Friedman.
That
I'm
going
to
kind
of
weave
in
here
was
that
the
particles
were
pushed
with
the
oilish
step
and
we
did
do
upwind
particle
pushing
in
this
case.
C
C
So
the
the
main
reason
we
ended
up
doing
a
kinetic
Continuum
code
was
because
you
ended
up
with
the
ion
Cloud
that
couldn't
be
described
very
well
with
fluid
codes
that
end
up
hold
up.
Sorry,
let
me
let
me
find
a
good
picture
here.
Okay,
this
isn't
what
I
wanted
and
I
know
it's
hidden
somewhere
in
my
backup,
slides
if
I'm
start
here
so
for
the
ion
distribution
space,
you
end
up
getting
a
acceleration.
Collision
fly
health
events.
C
C
You
end
up
with
a
large
trapped
cloud
of
cold
ions,
so
you
could
imagine
I'm
going
to
do
some
annotation,
which
is
always
dangerous,
so
bear
with
me
everyone
you
have
your
typical
scl
light
configuration,
which
is
this
ion
distribution,
that's
accelerated
towards
the
wall,
but
you
can
end
up
forming
a
large
cloud
of
non-thermal
ions
near
the
surface,
which
motivated
our
choice.
To
use
this
kind
of
scheme
was
to
resolve
these
kinetic
effects,
specifically
as
well
as
introduce
our
volume
effects.
C
E
Well,
you
want
me
to
talk.
Yes
go
ahead,
oh
my
god,
collisionless
Blast,
Off
codes,
you
know,
Continuum
codes
are
pretty
notorious
for
filaments
in
as
time
goes
on,
like
I
said,
collisions
mitigate
that
you
know
it's
the
lore,
it's
embedded
in
the
literature
and
continue
kinetic
codes
that
that
happens.
But
so,
if
your
code
was
going
to
have
problems
in
that
respect,
it
would
have
it
would
have
surfaced
and
you
would
have
stopped
you
in
your
tracks
and
you'd
have
to
have
done
something
so
I
take
the
answers.
B
G
I
I
have
a
question
to
you.
When
we
looked
at
this
particular
cell
codes,
we
saw
a
lot
of
isolations
right,
I,
don't
know
if
you
saw
right
Mike's.
Another
physical
reflector
was
on
explaining
cancellations
when
distribution
functions,
right
changes
and
that
changes
the
potential
it
kind
of
self-coupled
into
oscillations.
That
may
require
some
kind
of
at
least
Heating
in
the
system
and
I'm
just
curious.
If
you
plan
to
do
that
or
source
of
external
and
your
code
to.
C
C
G
F
Yeah
Alex,
so
in
in
the
particle
code
we
see
long-lasting,
oscillations
and
I.
Wonder
typically,
Continuum
codes
can
be
diffusive
and
smear
out
things
and
maybe
do
some
damping
of
oscillations,
and
you
may
be
seeing
some
of
that
and
that
may
explain
some
of
the
difference.
Also
Mike
privately
answered
the
question.
I
posed
the
the
performance
Criterion,
the
sort
of
number
of
cells
pushed
not
number
of
particles
pushed
okay.
F
C
D
B
D
C
C
You
would
end
up
getting
a
current
limited
sheath
that
would
end
up
being
limited
by
just
the
electrons.
It
looks
something
like
this:
the
ions
end
up
filling
if
you
can
see
the
doodle,
hopefully
on
the
plot
C
for
the
potential.
So
without
ions
you
end
up
with
a
potential
minimum
and
current
density
limited
sheath
once
you
have
ions,
you
end
up
collapsing
this,
because
the
ions
can
spread
out
in
this
potential.
Well,
so
what's
happening
in
this
next
plot.
Is
that
you
have?
C
D
C
C
So
yes,
well,
what
you
end
up
getting
is
what
I
just
described
as
a
process.
That's
a
limit
limiting
the
amount
of
net
current
density
that
you
can
get
in
case
three
or
like
0.3
here
your
potential.
If
you
increase
the
potential
of
this
probe
here
relative
to
the
outer
sheath
by
say
another
factor
of
two,
you
would
find
that
the
plasma
potential
would
be
dragged
pretty
closely
with
the
surface
potential
and
it
would
increase
slightly
between
the
Surface
potential.
I,
keep
losing
my
cursor
here.
C
Sorry
about
this
between
your
surface
potential
and
your
plasma
potential,
so
that
would
be
to
suppress
any
farther
electron
emission
from
the
surface,
while
also
limiting
the
amount
of
a
mission
that
you
can
end
up.
Having
so
it'll,
look
eventually
like
a
straight
line
between
the
two,
this
sheath
will
expand
to
be
the
whole.
You
know
pretty
much
kind
of
the
whole
distance
between
the
two
plates
and
you'll
be
suppressing.
All
of
the
current
trying
to
get
out
from
the
surface.