1. Conceptual Study for the Dynamic Control of Fusion Power Plant
J. S. Kang, K. J. Chung, S. Choi,
and Y. S. Hwang
NUPLEX, Dept. of Nuclear Engineering, Seoul National University, 599, Gwanak-ro, Gwanak-gu, Seoul , Korea

2. General comparison of fission and fusion power plant system
Contents
Introduction
General comparison of fission and fusion power plant system
Tokamak system code
Dynamic control concept model

3. Introduction
In order to realize nuclear fusion as a future energy source, fusion power plant study is essential.
Dynamic control of fusion power plant has not been studied so far
Study on fusion reactor dynamic control is a critical element to complete fusion energy development.
[2] F. Najmabadi , Fusion Engineering and Design 65 (2003)
[1] D. Maisonnier et al, Power plant conceptual studies in Europe, Nucl, Fusion 47(2007)

4. General Comparison of fission and fusion power plant - Nuclear fission power plant system
Basic Strategy
Nuclear reactor operation control system analysis        
- Nuclear reactor core control system.
Analysis of core neutron dynamics
- Relationship between nuclear reactor thermal output and neutron behavior.
Fission reactor core produce an atomic energy.
Primary loop system transfer fission thermal energy to secondary loop through heat conduction
Heated secondary loop water vaporizes to make steam turbine work.
Condenser has a role of cooling secondary loop water with sea water
<Overall schematic diagram of Fission reactor system – Black rods in reactor core are control rod.>

5. General Comparison of fission and fusion power plant - Nuclear fission power plant system
Nuclear power plant operation control system can be classified according to measurements such as neutron flux, temperature, pressure, and water level.
Thermal energy from fission reactor per unit volume and unit time can be expressed
energy per fission reaction(κ), neutron flux distribution(Φ), and fission cross section(Σ).
Neutron equilibrium relation in steady state operation
Neutron production rate = leakage neutron + absorbed neutron
Concentrate on only thermal neutron, neutron diffusion equation can be
Then thermal power density distribution and thermal power inside fission reactor core is from fission reaction equation.
Carbon rod control neutron flux but also fission reaction rate -> control knob

6. General Comparison of fission and fusion power plant - Nuclear fusion power plant system
Plasma
Turbine
Heating
Current Drive
Magnets
Cryogenics
BOP
Blanket, Shield M
To Grid
Recirculating Power
[1]
Pearson Coil
Fusion power equation which uses deuterium and tritium fuel can be expressed
fusion power is mainly concerned with fuel density and temperature. Cross-section for DT fusion reaction in a certain density and temperature condition is the same. Neutron does not directly participate in fusion reaction. fusion power is mainly concerned with fuel density and temperature.
[1] B.G. Hong et al, Fusion Engineering and Design, Vol 83(2008)

7. General Comparison of fission and fusion power plant - Comparison
unstable
stable
A deterioration of confinement with increasing temperature is a stabilizing effect for alpha particle heating. [3]
Reactivity and power profile. [2]
Steady state operation
Subcritical
Multiplication
Neutron flux control
Criticality
Start up
Inertial current drive heating
Ignition
Fueling and auxiliary heating
[2] MIT Open Courseware Nuclear Power Plant Dynamics and Control
[3] J. Wesson, Tokamaks second edition, Clarendon press(1997), page 15

8. Tokamak system code
System Code – Calculate physics and engineering parameters of Tokamak with theoretical and empirical formulas.
<Role of System Code>
Design of
new experimental device
Tokamak Reactor System Analysis
Design and performance study
of fusion power plant
Dynamic Simulator ?

9. Tokamak system code Solve simultaneous equations for n variables
(Physical parameters or device parameters)
Usually, the number of variables exceeds the number of equations.
Provide operating spaces as constraints
to obtain a particular plasma state via control
   Constraints
     Variables  
Power balance and confinement time
Alpha and aux. heating power and energy losses
Density limit
Electron density
Beta limit
Pressure = density * temperature
Safety factor
Bootstrap current fraction, current drive power

10. Physics Modeling Plasma Elongation Using Menard formula the maximum κ
Safety factor
- number of toroidal rotations per poloidal rotation of a field line
Scaling for ST plasma(Wong formulation)
Plasma Current

11. Physics Modeling Beta Limits
According to Menard an appropriate limit on Plasma Beta
Lin-liu formula
Toroidal Beta
Poloidal Beta

12. Physics Modeling Density
Density limit is given by greenwald limit at core region
Borass limit at edge region
Temperature
- ion and electron temperature and densities are related to pressure
- After numerical integration , density and pressure.
then

13. Physics Modeling Neutral Beam Injection Energy
assume that parobolic-like deposition profile with tangential injection at R0
beam distance
Current Drive Efficiency
from Start and Cordey fitting result
Current Drive Power
current to be driven is [plasma current*(1-bootstrap fraction)]
therefore

14. Physics Modeling Plasma Power Balance Equation
Electric power conversion coefficient is set to constant value.
[1]
[2]
[2]L.M. Hively, “Convenient Computational Forms for Maxwellian Reactivities”,
Nuclear Fusion, 17, p (1977)
[1]S. Glasstone and R.H. Loveberg, Controlled Thermonuclear Reactions (Van
Nostrand, New York, 1960), Chapt. 2.

15. System code result
Fusion power Q
Low
Q value
Beta
Limit
Region
Fusion power and Q value vs Elongation R=4m, A=1.5
Elongation can represent a magnitude of plasma shaping. Elongation range is determined by bootstrap current and Menard limit.
Elongation value increase, fusion power and Q value tendency is opposite.
Fusion power change is not so severe than Q value. In this calculation result, elongation value around 2.8 is favorable.

16. System code result
Fusion power Q
Fusion power and Q value vs Plasma current, Maximum elongation conditon
R=4m, A=1.5
Plasma current provides basic Tokamak operation condition.
Then,. Figure 4 shows tha reactor Q value would decrease
high plasma current is not a recommendable operation condition.

17. Dynamic Control Concept
Strategy to make analysis model of fusion reactor
Static Analysis with System Code
Cross check viability and performance spaces of fusion reactor
Dynamic Analysis starting from magnetic and kinetic controls for basic plasma parameters (equivalent to neutron kinetics in fission)
Find major parameters which can affect fusion reactor performance

18. Dynamic Control Concept
Major fusion reactor core control parameters
Plasma current
Provide basic tokamak operation condition.
Plasma position and shape
Largest cross section area, D-shape cross section has better performance.
Auxiliary heating
To heat the plasma to millions of degrees until ignition for self-heated fusion processes.
Fueling
Control fusion power within plasma density and pressure limits.
Build a simple fusion power simulator.

19. Dynamic Control Concept
current drive power is not needed in reactor operation regime as in figure
-> main control knob which is equivalent to a carbon rod should be gas puffing system (fueling).
operator controls magnitude of fuel -> constrained variables would be changed -> density, temperature, and fusion power also vary.
Operator will set these variables with limited regime to obtain a proper fusion power. This procedure will make dynamic control of fusion reactor possible.