Introduction to Nuclear Fusion -...
Transcript of Introduction to Nuclear Fusion -...
![Page 1: Introduction to Nuclear Fusion - ocw.snu.ac.krocw.snu.ac.kr/sites/default/files/NOTE/INF-2017-10-Pinch.pdf · jz j0 IP Sa for r a r a I B P 2 0 2S P T. 19 Helical kink instability](https://reader030.fdocuments.us/reader030/viewer/2022020206/5e03f8c48f6dcc712c5c85e5/html5/thumbnails/1.jpg)
Introduction to Nuclear Fusion
Prof. Dr. Yong-Su Na
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To build a sun on earth
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To build a sun on earth
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• Bring the Sun on the Earth
Quantity ITER Sun Ratio
Diameter 16.4 m 140x104 km ~ 1/108
Central temp. 200 Mdeg 15 Mdeg 10
Central density ~1020/m3 ~1032/m3 ~1/1012
Central press. ~5 atm ~1012 atm ~1/1011
Power density ~0.6 MW/m3 ~0.3 W/m3 ~2x106
Reaction DT pp
Plasma mass 0.35 g 2x1030 kg ~1/1034
Burn time const. 200 s 1010 years ~1/1015
M. Kikuch, “steady state tokamak reactor and its physics issues”, Talk at SNU, Korea, September 30, 2011
Magnetic Confinement
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To build a sun on earth
- Open magnetic confinement - Closed magnetic confinement
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What is open magnetic confinement?
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• Equilibrium – Radial Force Balance
X Jz
Bθ
Jz x Bθ
X Bz
Jθ
Jθ x Bz
BJp
JB
0
0 B
p BJ
Open Magnetic Confinement
http://lasp.colorado.edu/education/outerplanets/solsys_star.php
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Z pinch θ pinch screw pinch
Magnetic mirror
Open Magnetic Confinement
http://phys.strath.ac.uk/information/history/photos.php http://www.frascati.enea.it/ProtoSphera/ProtoSphera%202001/6.%20Electrode%20experiment.htm
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What is Z-pinch?
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• The Z Pinch
Magnetic Pinch
J
B
X Jz
Bθ
Jz x Bθ
http://www.plasma-universe.com/Pinch_(plasma_physics)?title=Special:Booksources&isbn=0387975756 http://ask.nate.com/qna/view.html?n=6318216
G. Thomson and P. Thonemann
- The Lorenz force created by a lightning strike crushed this hollow lightning rod and led to the discovery of the pinch.
http://joiimg.tistory.com/416 http://www.thunderbolts.info/forum/phpBB3/viewtopic.php?p=731&sid=824cd77d679b252e92355fcbf212ed7a
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• The Z Pinch
Magnetic Pinch
http://joiimg.tistory.com/416 http://www.thunderbolts.info/forum/phpBB3/viewtopic.php?p=731&sid=824cd77d679b252e92355fcbf212ed7a
http://www.plasma-universe.com/Pinch_(plasma_physics)?title=Special:Booksources&isbn=0387975756 http://ask.nate.com/qna/view.html?n=6318216
G. Thomson and P. Thonemann
- The Lorenz force created by a lightning strike crushed this hollow lightning rod and led to the discovery of the pinch.
J
B
- The plasma carries an electric current and is confined by
the magnetic field induced by this current.
- As the current is increased, the larger magnetic field compresses
the plasma and also raises its temperature by Joule-heating.
- Confinement and heating is simultaneously provided.
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12 ZETA (1954-58, UK) P. C. Thonemann et al, Nature 181 217 (1958)
Magnetic Pinch • The Z Pinch X Jz
Bθ
Jz x Bθ
- The plasma carries an electric current and is confined by
the magnetic field induced by this current.
- As the current is increased, the larger magnetic field compresses
the plasma and also raises its temperature by Joule-heating.
- Confinement and heating is simultaneously provided. Where did the neutrons come from in ZETA?
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Large current produced by
capacitor
longitudinal plasma current
self field induced by JZ
Magnetic Pinch • The Z Pinch
J.P. Freidberg, “Ideal Magneto-Hydro-Dynamics”, lecture note
- Equilibrium
Sequence of solution of the MHD equilibrium equations
1. The ▽∙B = 0
2. Ampere’s law: μ0J = ▽xB
3. The momentum equation: JxB = ▽p
BJp
JB
0
0 B
How about the pinch effect in a electric cable/wire?
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0)(0
rB
dr
d
r
B
dr
dp0
2 0
2
0
2
r
BBp
dr
d
tension force by the curvature of the magnetic field lines
particle pressure + magnetic pressure force
Sequence of solution of the MHD equilibrium equations
1. The ▽∙B = 0
2. Ampere’s law: 0J = ▽xB
3. The momentum equation: JxB = ▽p
01
B
r
)(1
0
rB
dr
d
rJ z
dr
dpBJ z
Magnetic Pinch • The Z Pinch
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22
0
2
2
0
2
2
00
22
0
2
2
00
2
0
2
00
)(8
)(
2
rr
rIp
rr
rIJ
rr
rIB
z
- The magnetic pressure and plasma pressure each produce
positive (outward forces) near the outside of the plasma.
- The plasma is confined by magnetic tension.
- It is the tension force and not the magnetic pressure
gradient that provides radial confinement of the plasma.
Bennett profiles
(Bennett, 1934)
X Jz
Bθ
Jz x Bθ
Magnetic Pinch • The Z Pinch
02 0
2
0
2
r
BBp
dr
d
J.P. Freidberg, “Ideal Magneto-Hydro-Dynamics”, lecture note
http://scienceray.com/technology/industry/where-do-rubber-bands-come-from/
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Magnetic Pinch
- Cylindrical co-ordinates: Specify current profile
drdpBz
j / , ,
)2
/(0 aPIjzj for ar
• The Z Pinch
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Magnetic Pinch • The Z Pinch
2
0
2
2
00
0
0
0
0
222
)(2
2
1
a
rI
a
rI
r
rI
rrdjr
rrdjr
rB PP
rr
ra
IB P
2
0
2
for ar
r
IB P
2
0 for ar
jrBrr 0
)(1
- Ampere‘ law:
)2
/(0 aPIjzj for ar
a
r
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Magnetic Pinch • The Z Pinch
→ general result for the z-pinch, not dependent on profiles.
- Calculate , we find 2
0
)(
2
aB
pp
1p
- Compute force balance:
ra
I
a
IBj
dr
dp PPz 2
02
2
Boundary condition p(a)=0:
2
142
2
20)(
a
r
a
PI
rp
)2
/(0 aPIjzj for ar
ra
IB P
2
0
2
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Helical kink instability
Sausage or pinch instability
Magnetic Pinch • The Z Pinch
A. A. Harms et al, “Principles of Fusion Energy”, World Scientific (2000)
- A number of linear Z-pinch experiments were constructed during
the early years of the fusion program.
- Large currents of ~0.1 MA are needed thus rendering the Z pinch
to operate only in short pulses.
- Exhibiting disastrous instabilities, often leading to a complete
quenching of the plasma after ~1-2 μs.
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"kink instability" in one of the earliest Z-pinch devices, a pyrex tube used by the AEI team at Aldermaston, or earlier while still at Imperial College
Magnetic Pinch • The Z Pinch
- A number of linear Z-pinch experiments were constructed during
the early years of the fusion program.
- Large currents of ~0.1 MA are needed thus rendering the Z pinch
to operate only in short pulses.
- Exhibiting disastrous instabilities, often leading to a complete
quenching of the plasma after ~1-2 μs.
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21 θ-direction tension for equilibrium, z-direction tension for stability
Magnetic Pinch • The Z Pinch
- A number of linear Z-pinch experiments were constructed during
the early years of the fusion program.
- Large currents of ~0.1 MA are needed thus rendering the Z pinch
to operate only in short pulses.
- Exhibiting disastrous instabilities, often leading to a complete
quenching of the plasma after ~1-2 μs.
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What is θ-pinch?
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• The θ Pinch
Magnetic Pinch
externally
driven
induced
diamagnetic current
X Bz
Jθ
Jθ x Bz
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→ Force balance
→ Ampere‘s law
→ Closed magnetic field lines
BJp
JB
0
0 B
• Plasma Equilibrium
kinetic pressure balanced by JxB (Lorentz) force
2,nqB
Bpv pD
2,,B
pBvqnvqnJ eDeeiDii
Diamagnetic current
0 pJ
0 pB
- If B is applied, plasma equilibrium can be built by itself due to
induction of diamagnetic current.
Magnetic and Kinetic Pressure
induced by the pressure gradient: causing a decrease in B → diamagnetism
B
ion
←∇p
x
BJp
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Magnetic Pinch
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• The θ Pinch
Magnetic Pinch
externally
driven
induced
diamagnetic current
J.P. Freidberg, “Ideal Magneto-Hydro-Dynamics”, lecture note
X Bz
Jθ
Jθ x Bz
- Equilibrium
Sequence of solution of the MHD equilibrium equations
1. The ▽∙B = 0
2. Ampere’s law: μ0J = ▽xB
3. The momentum equation: JxB = ▽p
BJp
JB
0
0 B
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02 0
2
zB
pdr
d
0
2
0
0
2
22 BB
p z
- At any local value of r, the sum of the particle pressure and the magnetic pressure
is a constant, equal to the externally applied magnetic pressure.
- The plasma is confined radially by the pressure of the externally applied magnetic field.
Sequence of solution of the MHD equilibrium equations
1. The ▽∙B = 0
2. Ampere’s law: 0J = ▽xB
3. The momentum equation: JxB = ▽p
0
z
Bz
r
BJ z
0
1
dr
dpBJ z
Magnetic Pinch • The θ Pinch
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2
000 /2 Bp
2/122
00
22
0
)]/exp(1[
)/exp(
arBB
arpp
z
- Typical example
Magnetic Pinch • The θ Pinch
J.P. Freidberg, “Ideal Magneto-Hydro-Dynamics”, lecture note
0
2
0
0
2
22 BB
p z
- The plasma is confined radially by the pressure of the externally applied magnetic field.
Plot the forces.
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- One of the early successes of the fusion program in terms of
the performance.
- Ti ~ 1-4 keV, n ~ 1-2x1022 m-3, β(0) ~ 0.7-0.9
- High temperature using the implosion heating method:
rapidly rising magnetic field acting like a piston
- No indication of macroscopic instability (neutrally stable)
- Severe end loss (τ ~ L/VTi, e.g. 10 μs for a 5 m device)
Magnetic Pinch • The θ Pinch
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What is screw pinch?
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• The General Screw Pinch
- A hybrid combination of Z pinch and θ pinch
- This combination of fields allows the flexibility to optimise
configurations w.r.t. force balance and stability.
Magnetic Pinch
X Jz
Bθ
Jz x Bθ
· Bz
Jθ
Jθ x Bz
- Equilibrium
Sequence of solution of the MHD equilibrium equations
1. The ▽∙B = 0
2. Ampere’s law: μ0J = ▽xB
3. The momentum equation: JxB = ▽p
BJp
JB
0
0 B
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- Sequence of solution of the MHD equilibrium equations
1. The ▽∙B = 0
2. Ampere’s law: 0J = ▽xB
3. The momentum equation: JxB = ▽p
01
z
BB
r
z
)(1
0
rB
dr
d
rJ z
dr
dpBJBJ zz
r
BJ z
0
1
02 0
2
0
22
r
BBBp
dr
d z
- Even though the equations are nonlinear, the forces superpose because of symmetry.
Magnetic Pinch • The General Screw Pinch
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- Because of its flexibility the general screw-pinch relation describes
a wide variety of configurations.
Magnetic Pinch • The General Screw Pinch