Tritium burnup fraction

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					Tritium burnup fraction

            C. Kessel, PPPL

ARIES Project meeting, July 27-28, 2011
           Gaithersburg, MD
                     Tritium burnup fraction
For MFE we must inject more tritium into the plasma chamber than is consumed in
fusion reactions, because all the fuel is not consumed before it is pumped out of
the chamber

The rate at which all different particles are pumped out of the chamber is
determined so that we do not get a build up of He (product of D + T) and
impurities, and the fusion power is what we desire

ST = nDnT<σv> + nT/τT* simple balance of tritium density inside the plasma

The burnup fraction is the ratio of the amount of tritium consumed in fusion
reactions every second to the total tritium we lose every second, this is always < 1.0

fb = nDnT<σv> / (nDnT<σv> + nT/τT*)
                                                   We do not know what to assume
Any value of burnup fraction is not accessible, since we must keep the density of He
                                                   for this
and other impurities sufficiently low

nHe/τHe* = nDnT<σv> balance of He density inside the plasma
                                Tritium burnup, cont’d
                                        For a power plant, using only τT* = τT we can get
                                        a lower bound to fb, which is about 5.6%
fb 
                     1                  If we assume τT* = 5 xτT, we get 23%
            n D  T * v   DT           If we assume τT* = 10 xτT, we get 37%

                                         1         19.94 
v     DT
            (m /s)  3.68 10
              3                   18
                                               exp 1/ 3      Ti is in keV
                                        Ti         Ti 
                                                  From experiments, the once through
                                                  particle confinement time is about the
 Volume average density
                                                  same as the global energy
 <nD> ~ 0.8-1.25x1020 /m3                         confinement time
                                                  τT ~ τ E
 Volume average temperature                       To include tritium re-entering the
 <Ti> ~ 20 keV                                    plasma, its total particle confinement
                                                  time is larger than the once through
 Global energy confinement time                   particle confinement time
 τE ~ 2 s                                         τT* > τT , often expressed as τT /(1-R),
                                                  where R is a recycling coefficient,
                                                  which is a severe simplification of the
Experiments indicate that the residence time of He in the plasma
before being pumped out of the plasma chamber (τHe*), and hydrogen
is expected to be similar (τHe* ~ τT* ~ τD*), is about 3-10 x τE, with the
lower values well established
     Measurements of the He density in the plasma are made, so the
     time constant for the decay of this helium density are made after
     the source (He neutral beam) is turned off
     The τHe*/τE, decreases with increasing plasma density, since the
     recycling of the He back into the plasma, from the walls, is decreased

It is possible to get preferential removal of DT fuel relative to He, or
visa versa, based on atomic physics in the divertor, but this is observed
to be quite variable
      In experiments this is described by (nHeo/2nD2o) / (nHe/ne) , that is a
      ratio of helium gas relative to hydrogen in the divertor, divided by
      the helium ion density relative to electron density in the plasma

We want this total residence time to be short enough that the helium
concentration in the plasma is not too large, BUT we also want to take
any credit for fuel (D and T) to re-enter the plasma and undergo fusion,
so we like it to be longer if possible and increase our T burnup fraction
                    Tritium burnup fraction
We also introduce impurities to help radiate power, while other impurities will
come from eroded materials inside the plasma chamber

The He and impurities reduce the fusion power by diluting the D and T fuel

There are densities of these “pollutants” that we can tolerate, and this will
determine a self-consistent balance of all particles in the plasma, and the
injection of fuel and impurities, and the pumping of fuel, He, and impurities

In the plasmas we are always quasi-neutral ne = nD + nT + 2nHe +ΣiZinZ,i

The physics of the particles inside the plasma chamber is a bit more complicated
that this….

The plasma particles diffuse out of the plasma and enter a region between the
plasma and the solid material wall, we call the scrape off layer

The particles can diffuse to the first wall or flow into the divertor, they impact
the solid walls and re-emerge as neutral atoms
Some of these particle can also be absorbed or implanted into the FW or divertor,
or pumped out of the chamber through the divertor

The neutral atoms can find their way back to the plasma and re-enter it, quickly
becoming ionized

This re-entering population can bring unburned fuel (D and T) back where it could
undergo fusion… when we try to figure out how much time a tritium ion spends
in the plasma we must include this effect

How efficiently particles from the scrape off layer can fuel the plasma is a critical
research area, we characterize this by the neutral penetration depth, which means
how far into the plasma does a neutral atom get before it is ionized

We know that fueling from the edge is always going on, but we also know that this
fueling can be reduced by operating the plasma with high densities, typical of the
values we want in a fusion power plant (even ITER will get to this level)…..this is
called screening

So low density plasmas typically have high edge fueling efficiencies (or high neutral
penetration), and high density plasmas have low edge fueling efficiencies (or short
neutral penetration)
    Tritium burnup fraction, Tritium ions becoming atoms
                                     after hitting a material wall
             cont’d     Tritium ions go to the                       wall
                                       divertor and hit the
                                       divertor surface
If a particle is ionized near the      becoming atoms, and
plasma edge, it has a good chance      some re-enter the
of just diffusing back out of the      plasma
plasma, and not getting into the
hot center of the plasma where
fusion is going on
Recall some of the particles end up                injection,
in the divertor where they are                     deep
pumped out of the plasma                           penetration
chamber, and there may be
preferential pumping of some types
of particles relative to others
depending on atomic physics in the
                                    Neutral tritium atoms re-
                                    entering the plasma, weak
                       Some basic definitions
ST = source term for tritium (fueling source)

nDnT<σv> = fusion reaction rate, consumption of tritium

τT = mean time a triton that is injected into the plasma (pellet) takes to leave the
plasma (how long does a triton that is deposited deep in the plasma take to get out)

τT* = mean time a triton that was originally injected into the plasma (pellet) spends
in the plasma before being pumped out of the plasma vacuum chamber

                     dnT                        n
Balance in                ST  n D nT  v   T
the plasma            dt                       T *
The term nT/τT* is the loss of tritons from the plasma before they undergo fusion

The time constant τT* looks simple but actually represents a mean time spent
inside the plasma, which is very hard to measure, while having hidden in it

    the particle transport time inside the plasma (τT)
    the pumping of tritons out of the plasma chamber
    the recycling of tritons from the wall
    the neutral penetration distance from the plasma edge into the plasma
    the depth that a tritium ion penetrates toward the hot plasma center after
    re-entering the plasma from the edge
    the implantation and subsequent loss of tritons thru the FW or divertor

    It is normally written as τT* = τT / (1-R), where R is the recycling coefficient
    (although it actually has all the other physics in it too from above)
Reiter, et al, examined the allowed helium concentration in a plasma for DT
fusion in 1990, and also derived a particle confinement time that accounted
for the physics that we expect to be governing this situation, albeit for
He….but we expect the same physics to govern the hydrogen isotopes as

With this basic physics picture in mind, we can derive an expression for the time
constant, τHe* or τT*

τHe* = τHe,1 + (Reff/(1-Reff)) τHe,2 Reff/(1-Reff) is the mean # of recycling events back
into the plasma experienced by the particle before being pumped

The τHe,1 is the mean time a He ion spends in the plasma after being produced from
a fusion reaction (its first introduction to the plasma), this is typically ~ τE

The τHe,2 is the mean time a He ion spends in the plasma after re-entering from the
plasma edge region, which is expected to be < τE

Some fairly old simulations for ITER indicated that τHe,1 ~ 8 s, while τHe,2 ~ 0.5 s, using
a transport model in BALDUR
Some other efficiencies can be defined to help relate our expression to real systems,
and uncover the physics in the effective recycle coefficient, Reff

Exhaust efficiency = 1-Reff, probability a particle will be pumped whenever it crosses
the plasma boundary in outward direction

εcoll = collection efficiency, εcollφout fraction of particles leaving plasma that are
collected by pumping system, and (1-εcoll)φout hit the wall

εrem = pump removal efficiency, εremεcollφout fraction of particles leaving plasma that
are collected by pumping system and pumped away

εpump = exhaust efficiency = εremεcoll, so εremεcollφout are removed from the plasma

R(1-εcoll) φout particles will recycle from the wall (R is the true recycling coefficient)

(1-R) (1-εcoll) φout will be absorbed in the wall (whether it is implantation or other

γ = refueling efficiency of recycled particles
τHe* = τHe,1 + (Reff/(1-Reff)) τHe,2

τHe* = τHe,1 + γ[R(1-εcoll)+εremεcoll]/{1- [R(1-εcoll)+εremεcoll]} τHe,2

γ<< 1, low re-fueling efficiency

R ~ 1, stationary wall conditions
                                                             τHe* = τHe,1
εcoll = 0.5

εrem = 0.02

γ~ 1, high re-fueling efficiency
                                                             τHe* = τHe,1 + τHe,2
Others the same
     Further efforts on tritium burnup fraction

• Relate these quantities back to fueling and pumping rates, and neutral gas
  enrichment in divertor

• Examine more experimental results, gather results together

• Simulation results? B2-Eirene?

• Correlate the re-entering tritium with a probability of fusion depending on

• Model expansion to include more stuff
             Use 2 population model for tritium
                                      dnT1                             nT1
                                              ST  n D nT1  v  
                                       dt                              T1
dnT                         nT
     ST  n D nT  v  
 dt                        T *
                                      dnT2        nT1                        nT2        nT2
                                           R          n D nT2  v           R
                                       dt         T1

   nT1 = density of original tritons injected via pellets into the plasma
   nT2 = density of tritons which subsequently left the plasma and re-entered via
   nT = nT1 + nT2          
   τT1 = mean residence time for tritons originally injected via pellets
   τT2 = mean residence time for tritons that re-enter the plasma via recycling
   R = an effective recycling coefficient, it contains other physics besides just

   Assume nD is fixed, although it would follow similar equations, and introduce a
                        2 population model, cont’d

                       ST  T1
         nT1                           ST  T1 (1 f b1 )
                 1 n D  T1 v
                  nT1 R T2              1              nT1 R T2 (1 f b2 )
         nT2                                       
                  T (1 R)           n D  T2 v           T (1 R)
                                 1                           1

                                        (1 R)

                                  T2 R(1 f b2 ) 
         nT  ST (1 f b1 ) T1                   
                                      (1 R) 
    Including an original pellet fueling efficiency ηf, then

                                 f (1 f b1 )(1 f b2 ) T2 R (1  f )(1 f b2 ) T2 
    nT  ST  f (1 f b1 ) T1                                                        
                                          (1 R)                      (1 R)           
Just the same as we have for helium, τT,1 ~ τE

and τT,2 < τE

Unfortunately, this global particle model does not tell us the probability that the re-
entered triton has of getting into the hot fusion zone in the plasma center


The chance of experiencing a fusion event regardless of where it is in the plasma

We don’t know where it gets to, this is a particle transport question

We might characterize this with the neutral penetration depth and the local fusion
reactivity associated with that depth

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