Physics of fusion power_1_

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					Physics of fusion power

      Lecture 12: tokamak – continued
A tokamak

n   Plasma (purple) Notice the
n   Surrounded by plates
n   Vessel (pumps)
n   Coils mostly outside vessel
    (finite reaction time)
n   Ohmic transformer /
    toroidal field coils (green)

                                   Schematic Drawing of the poloidal cross
                                   section of the ASDEX Upgrade tokamak
The tokamak

n   Magnetic surfaces are the
    surfaces traced out by the
    magnetic field
n   They are nested (best
n   Centre is shifted outward
n   Large passive coils
n   Magnetic field ends on a
    set of plates
n   Large set of small coils for
    diagnostic purposes

                                   Schematic Drawing of the poloidal cross
                                   section of the ASDEX Upgrade tokamak
Reason 1 for plasma elongation
n   Plasma can be diverted onto a
    set of plates
n   Close to the coils the field of
    the coils dominates
n   In between the field is zero
    resulting in a purely toroidal
    field line
n   This shows up as an X-point in
    the figure of the magnetic
n   Surfaces outside the one with
    the X-point are not close with
    the field ending on the plates
                                      Shaping coils allow for plasma to be
                                      diverted onto the divertor-plates
Plasma limiter
n   Without divertor the plasma
    needs to be limited by a
    material (referred to as
n   The plasma touching the
    limiter is still several 1000
    of Kelvin
n   Sputtering or melting leads
    to the release of material
    into the plasma
n   These unwanted                  Schematic picture of a plasma limiter
    components are referred to
    as impurities
Impurities are no good news

n   Given a fixed electron density, impurities dilute the fuel
                                 Density of the impurity with charge Z

n   Acceleration of electrons by the ions in the plasma lead to
    radiation losses known as ‘Bremstrahlung’

                           Effective charge
n   The radiation scales with the average charge. High Z
    impurities enhance the radiation
n   High Z-impurities also lead to energy loss through line
Preventing impurities
n   Plasma facing
    components have to be
    chosen carefully
n   Carbon / Beryllium have a
    low Z
n   Carbon does not melt but
    has the problem that it
    binds well with Tritium
    (contamination of the
n   Tungsten has very high Z,
    but takes the heat loads
    very well
n   Using a divertor the particles
    that leave the plasma flow
    along the magnetic field and
    hit the target plates
n   These plates are far away
    from the plasma such that any
    impurity released at the plate
    has a smaller chance ending
    up in the plasma
n   Furthermore, one can try to
    cool the plasma further
    through special arangements
    in front of the plates

                                     Plasma flow in divertor configuration

n   The divertor has a
    disadvantage : it takes
n   In general only one divertor
    is used, usually at the
    bottom (easier to construct)
Picture of the plasma

n   Shows that most of the line
    radiation (one of the lines
    of Hydrogen) comes from
    the divertor structure
n   Real plasma so hot that it
    does not have Hydrogen
    line radiation
n   So thin that you look right
    through it
The divertor
n   A modern divertor design
    looks something like this
n   Note that it has, as far as
    possible a closed structure.
    This to allow the efficient
    pumping of the neutral
n   Note also that the angle
    between the magnetic field
    and the plate is as small as
    possible. This makes that the
    energy carried by the particles    Modern divertor design (ITER)
    to the plate is distributed over
    the largest possible area
Reason II : Plasma elongation
n   Distance to go around
    poloidally is larger

    For the same plasma current

n   If q = 3 is the limit of operation
    one can run a larger current in
    an elliptically shaped plasma
Reason III : Plasma elongation

n   A transition phenomenon is
    observed in Divertor
    plasmas known as the L
    (low) to H (high
    confinement) transition
n   In this transition a steep
    pressure profile is
    generated at the plasma
n   Not very well understood
n   Confinement improvement
    is roughly a factor 2 !!!!
Equilibrium / Vertical instability
n   Magnetic field due to the coil
    follows form

n   Assume d<<R one finds

n   This leads to a force on the
Vertical stability

n   Integrating the force

n   Thus
Vertical stability

n   Forces

n   Equilibrium requires

n   Such that the forces
Vertical stability

n   The forces

n   Are in equilbrium when the
    coil currents are the same.
n   But when the plasma is
    shifted upward by a small
    amount d
Vertical instability

n   Small shift d << d

n   When total mass of the plasma is M

                         Growth rate of the vertical instability
Back to the picture
n   Plasma vertical instability with
    growth rates of the order 106
n   For this reason the passive
    coils have been placed in the
n   When the plasma moves it
    changes the flux through the
    coils which generates a
    current that pushes the
    plasma back
n   Growth rate is reduced to the
    decay time of the current in
    the coils (ms)
Why more current?

n   One of the reasons is
    related to the equilibrium
n   The surfaces of the
    tokamak are shifted
Outward shift ???

n   The surfaces of the
    tokamak are shifted
n   This effect will be
    investigated starting from
    circular concentric
    surfaces, i.e. no outward
n   The pressure is constant
    on a magnetic surface
                                 Circular concentric magnetic
Outward force
n   Force = pressure x area
n   Considering the inboard
    and outboard side the
    areas are not the same

n   This lead to an outward

n   Equivalent to inflating a tire
The force leads to an outward shift

n   The pressure force leads to an outward shift
n   This shift compresses the surfaces on the outboard side
n   The poloidal magnetic field increases (distance between
    surfaces is smaller)
n   The increased tension and magnetic pressure can then
    balance the outward force
After some mathematics
n   The shift can be estimated to
    be roughly equal to

n   Where

                                    Picture of the Shafranov shift
n   Is the plasma beta connected
    with the poloidal field
But the shift can be too large

n   The solution stops to give a
    physically reasonable
    equilibrium when the shift is
    equal to the plasma radius

n   From which it follows

n   Loosely speaking it is only
    the poloidal field that
    confines the plasma
Relation between the beta values

n   The relation

n   Directly yields a maximum beta well below 1

                                Typical value 3
     Ratio of the field
     strengths is roughly 0.1

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