[Solutions] Introduction to Plasma Physics and Controlled Fusion Plasma Physics
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Plasma Physics and Fusion Energy Research
Paddy Mc Carthy,
Physics Department, UCC, 1/11/2011
Research Group: Plasma Data Analysis Group:
P. J. Mc Carthy (Group Leader)
R. Armstrong (Visiting Researcher)
PhD Students:
Diarmuid Curran
Mike Dunne (TCD graduate!)
Tom O’Gorman
MSc Students:
Brendan Cahill
Shane O’Mahony
Funders: Euratom, Max Planck Institut für Plasmaphysik, Munich
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Lecture Outline:
Plasma Overview
Fusion Energy and Tokamaks
How the Tokamak overcomes particle drift in a closed
axisymmetric system
Research topics in UCC
Fusion in Europe and further afield
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Plasmas are conductive assemblies of charged
particles, neutrals and fields that exhibit collective
effects, carry electrical currents and generate
magnetic fields.
What is a plasma?
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Why are we interested in
plasmas? •! Fusion Energy
–!Potential source of safe, clean, and abundant
energy.
•! Astrophysics
–!Understanding plasmas helps us understand
stars and stellar evolution.
•! Plasma Applications
–!Plasmas can be used to build computer chips
and to clean up toxic waste.
TCD Graduate Plasma Physics Module PY5012 Guest Lecture 1st Nov 2011
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per nucleon
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!" Fission is easiest at low energies; cross-section is maximum here
!" Fusion is vanisingly unlikely at low energies; cross-section is miniscule
TCD Graduate Plasma Physics Module PY5012 Guest Lecture 1st Nov 2011
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TCD Graduate Plasma Physics Module PY5012 Guest Lecture 1st Nov 2011
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Puzzle: T = 1keV at centre of sun.
Proton-Proton Coloumb Barrier height:
How can 1 keV protons overcome a 1 MeV barrier?
Answer: (Gamow, 1930) Quantum Tunnelling
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2He3 (0.82 MeV) + n (2.5MeV)
1D2 + 1D
2
1T3 (1 MeV) + p (3 MeV)
Relevant Fusion Reactions in the Laboratory
1D2 + 2He3
2He4 (3.6 MeV) + p (14.7MeV)
1D2 + 1T
3 2He4 (3.5 MeV) + n (14.1MeV)
3Li6 (7.4%) + n
2He4 + 1T3 + 4.8 MeV
3Li7 (92.6%) + n
2He4 + 1T3 + n – 2.8 MeV
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!
" 3#1020s m
$3
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It promises a large-scale energy source with basic fuels which are
abundant and available everywhere;
Very low global impact on the environment – no CO2 greenhouse gas
emissions;
Day-to-day-operation of a fusion power station would not require the
transport of radio-active materials;Power stations would be inherently
safe, with no possibility of “meltdown” or “runaway reactions”;
There is no long-lasting radioactive waste to create a burden on future
generations;
While development and capital investment costs are high, the marginal
cost of supply is expected to be negligible compared to that of energy
derived from fossil fuels.
Fusion Energy - Advantages
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Fusion reaction is difficult to initiate
High temperatures (millions of degrees) in a clean, high vacuum
environment are required;
Technically complex and high capital cost reactors are needed
More research and development needed to bring concept to fruition
The physics is well advanced, but but technological and material
challenges requiring a multi-decade sustained effort must be overcome.
Fusion Energy - Disadvantages
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Tokamak •! Donut shape
•! Unlike mirror, no end losses
because the field lines go
around and close on themselves
•! But major problem with
particle drift if magnetic field
lines are circular in form.
Schematic picture of the tokamak
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Particle Drift Recap…
Parallel motion
Gyration
ExB drift
Pololarization drift Grad-B and curvature drifts
General expression for the drift velocity of the guiding centres of
particles of charge q in a uniform B field and sub ject to an
additional force F:
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Trajectories of a 75 eV electron in a B ! field of 1 mT and
E # fields of 0 (top), 150 V/m (middle) and 1500 V/m (bottom).
Insight into drift motion
Left/right half-orbits are
symmetric, but up-
down half-orbits are
strongly asymmetric =>
particle travels more to
right than to left.
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Toroidal curvature*
•! The toroidal magnetic field
follows form
•! And therefore varies with
major radius R as
Top down view of the tokamak
Toroidal magnetic field coils
Next 5 slides based on Warwick University
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Toroidal curvature
•! The toroidal magnetic field has a gradient
•! Which leads to a combined curvature
and !B drift in the vertical direction:
From we get
Note that the sign
of the drift depends
on the sign of the
charge q !
ˆ R ˆ " ˆ Z
0 B 0
# B
R0 0
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Toroidal curvature
•! The drift
•! Leads to charge separation
•! Build up of an electric field
(calculate through the balance
with polarization)
•! And then to an ExB velocity
Poloidal cut of the tokamak.
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Toroidal curvature has its price
•! The ExB velocity
•! Is directed outward and will
move the plasma on the wall in
a short timescale (µs)
Poloidal cut of the tokamak.
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Remedy : a plasma current
•! A toroidal current in the plasma will generate a poloidal field (field lines short way round)
•! Combined toroidal and poloidal fields make helical field lines so that all particle orbits sample top/inside/bottom/outside regions.
•! Vertical !B drift still present, but helical field lines “short out” any tendency towards charge separation by accelerating electrons along the field line to maintain charge neutrality.
•! Charge separation no longer occurs and particles are well confined.
The field lines wind around helically .
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Blick in das Plasmagefäß von ASDEX Upgrade
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Cross-section of ASDEX Upgrade tokamak showing toroidal and poloidal field coils
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PDAG List of Collaborative Projects & Research Topics
ASDEX Upgrade Project
CLISTE Interpretive Equilibrium Code
Function Parameterization
MHD activity analysis to improve q profile identification
Thomson Scattering analysis: ECE comparison
Wendelstein 7-X Project
Fast recovery of W7-X equilibria
Transport and spectroscopy experiments using a DP machine
ITER diagnostic design studies: Group involvement in
Integrated Tokamak Modelling Taskforce
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Fluid Pressure
v. minor radius 100 kPa
-!p jxB !
R
Z
Fluid pressure gradient (outward force/V) balances inward pinch force/V: jxB = !p
Grad-Shafranov
equation: scalar,
weakly nonlinear PDE
Axisymmetry of tokamak
simplifies jxB = !p:
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Interpretive Equilibria: Finding an equilibium to match data
•! Regularize source profiles: choose a functional form with a
reasonable number of free parameters
•! Flexible form very desirable. Good choice: Cubic Splines
•! Initialize to a default current distribution (centred in vessel)
•! (i) Solve Poisson-like linear PDE for trial Jtor (R,Z) by a
least squares best fit to input experimental data which must
be expressible as a linear function of the free parameters
•! (ii) Construct updated flux function and find new plasma
boundary (we are solving a free boundary problem)
•! (iii) Construct updated Jtor (R,Z) using updated flux
surface topology and free parameter values.
•! Iterate steps (i)-(iii) until a convergence criterion is met
Interpretive Tokamak Equilibrium at IPP Garching: CLISTE
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Physics & Astronomy
Society, UCC
31/1/2006 TCD Graduate Plasma Physics Module PY5012 Guest Lecture 1st Nov 2011
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Equilibrium Magnetics only 12-knot spline model (28 fit parameters)
E18 ROE 13kA
flux loops B probes MSE Ped.Pres. J||Bneo " ne dl I SOL
#17151, 3.850s
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Magnetics & Q=1 & DCN+LID & ROE & MSE & YAR fit
E18 ROE 0.5 kA
#17151, 3.850s
flux loops B probes MSE Ped.Pres. J||Bneo " ne dl I SOL
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The Wendelstein 7-X Stellarator (under construction in Greifswald) TCD Graduate Plasma Physics Module PY5012 Guest Lecture 1st Nov 2011
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Physics & Astronomy
Society, UCC
31/1/2006
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Physics & Astronomy
Society, UCC
31/1/2006
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Physics & Astronomy
Society, UCC
31/1/2006
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Physics & Astronomy
Society, UCC
31/1/2006
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ne=1.1e17 m-3 Te=0.6eV PHe=9.6e-3mb
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ne=1.5e17 m-3 Te=0.4eV PHe=1.2e-2mb
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Physics & Astronomy
Society, UCC
31/1/2006
Four decades
of progress in
achieving
confinement
times* leading
to scientific
breakeven
*
!
" E =(3/2) p dV#Heating Power
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The Future of Fusion Energy Research: ITER"
ITER, the International Tokamak
Experimental Reactor is being
constructed at Cadarache, near
Aix en Provence, on a 10 year
timeframe for c. #7.5bn and will
operate for c. 25 y at projected
running costs of #7.5bn. "
SSP
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TCD Graduate Plasma Physics Module PY5012 Guest Lecture 1st Nov 2011
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R. Aymar, Nobel Symposium Stockholm, 2005
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Summary
Fusion offers one of the greatest hopes for a long-term solution to
the problem of a viable, environmentally friendly source for the
world’s future energy needs.
Fusion research is carried out within the framework of plasma
physics, a key current area of both fundamental and applied
research.
At UCC, we participate (both on and off-campus) in experiments at
major fusion labs in Germany and the U.K. as well as in ITER
design activities.
TCD Graduate Plasma Physics Module PY5012 Guest Lecture 1st Nov 2011