Bananelectrons🍌🍌🍌 Profile picture
Sep 6, 2022 27 tweets 8 min read Read on X
#Backtoschool

Let's talk about fundamentals of #FusionEnergy: plasma energy balance and Lawson criterion
Plasma energy balance is determined by the energy sources feeding the plasma and the energy losses cooling it down

For the plasma to remain stationary, the energy balance must be in equilibrium, i.e. the sources must compensate the losses
The total power produced by the D-T fusion reaction Pfusion is divided between the products of the reaction, the alpha particles, i.e. the helium nuclei (He), and the neutrons
The neutrons take away about 80% of the energy, while the heavier alpha particles, keep about 20%
Palpha : the main source of the plasma energy comes from the alpha particles
They are confined by the tokamak magnetic field, and give energy to plasma by collision
Pneut: neutrons are not sensitive to the magnetic field, since they have no charge, and thus escape quickly, without having time to give their energy to the plasma

They are stopped by the materials in the components surrounding the tokamak vacuum chamber
If the energy from the fusion reactions is not sufficient to compensate losses, it is necessary to supply energy from the outside to maintain the plasma using an additional heating system

This is the external power Pexternal
Plasma confinement by the magnetic field is not perfect: particles and heat diffuse from the plasma center towards the outside
The losses connected to this particles and heat transport are considerable

Plasma also cools by radiation according to different processes
The result of all these terms gives the total power lost by the plasma Plosses

The temporal variation of the plasma energy W may thus be written:
only the alpha particles give their energy to the plasma, the rest of the fusion power is dissipated into the components surrounding the plasma
So possible balance scenarios are:
The energy confinement time tE
is the characteristic time of decrease in plasma energy; in other words, it is the time taken by the plasma to empty itself of its energy content if the sources supplying it are abruptly cut off
this time has nothing to do with the pulse duration, which is determined by the capacities of the machine magnetic system or plasma instabilities
The amplification factor Q
This is the ratio between the power from fusion reactions and the external power supplied to the plasma by the heating systems
This figure thus qualifies the plasma’s energy balance. If it is higher than 1, more energy has been produced with fusion reactions than was necessary to supply to maintain the plasma
When Q = 1, i.e. the moment when the quantity of energy produced by the fusion reactions is equal to that supplied to maintain the plasma
This is an interesting stage from the scientific point of view, as heating of the plasma is then to a great extent done by the alpha particles and no longer nearly solely by the additional heating, which is close to the situation of the reactor
Ignition   
is the situation where the power supplied by the fusion reactions is enough on its own to compensate losses and where the external power can thus be switched off
This corresponds to an infinite Q amplification factor
The plasma is thus self-maintained like a candle, which, once it has been ignited by a match (external power), carries on fuelling itself
At stationary state (dW/dt = 0), we have the following energy balance:
The thermal energy of a D-T plasma is:
Supposing that our plasma is a mixture containing 50% Deuterium and 50% Tritium
and by obtaining from the plasma’s near neutrality and temperature is uniform
The fusion power is equal to the number of fusion reactions multiplied by
the energy given off by a fusion reaction
Let us go back to our energy balance. In a stable state (dW/dt = 0)
By replacing W and Pfusion by their respective expression, we obtain Lawson criterion🙀🙀🙀:
For ignition we have 1/Q~0, as Q ~ infinity:
In practical terms, for a reactor conditions to be able to produce energy from fusion reactions, a sufficiently hot (T) and dense (n) plasma must be confined effectively
Talking about triple product in terms of different way of confinement we see how they're differentiated by density, temperature and time of confinement

MFC - magtentic fusion confinment (f.e. tokamak)
IFC - inertial fusion confinement (f.e. laser)
GFC - gravitational (f.e.⭐)

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More from @bananelectrons

Apr 10, 2023
Let's go through a brief summary of the

Foresight study on the worldwide developments in advancing #FusionEnergy, including the small scale private initiatives
This study provides an analysis of the leading public and private fusion initiatives globally which has been used to generate 4 foresight scenarios for fusion development Image
The study provides a picture of the most common challenges and barriers to fusion development as well Image
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Feb 17, 2023
Great workshop👍👍👍
With insights from R. J. Hawryluk and @ScottCHsu
The big picture looks like this Image
Although we still have a lot of work to do Image
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Dec 26, 2022
I've got the great one from @unitusviterbo and @renfusion (stellarator approach):
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#FusionEnergy @martinkupp @formbar
The most critical aspect of tokamak power plants is their pulsed duty cycle, which includes long plasma-burn phases followed by fast dwells to remove ashes and dusts from the reactor chamber and re-load the central solenoid
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This allows to reach a high power conversion efficiency, due to possible coupling with a Brayton–Rankine Combined Cycle (CC) Image
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Sep 22, 2022
#ThursdayMoney 🧵

This week we got deep analysis of possible #FusionEnergy cost valuation with @JesseJenkins in the authors' list!🙀🙀🙀
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Read 27 tweets
Sep 5, 2022
Exascale supercomputers are exactly what current fusion research needs, explains Dr. Choongseok “CS” Chang, lead PI of multi-institutional multi-disciplinary U.S. SciDAC Partnership Center for High-fidelity Boundary Plasma Simulation, headquartered at @PPPLab
One of the biggest current challenges is making accurate predictions about the processes that occur inside tokamak reactors, which use giant magnetic fields to confine plasma fuel in a torus shape to achieve the conditions necessary for fusion
To advance this science, Chang’s team is preparing to use the Aurora Exascale supercomputer, the country’s first Intel-architecture-based exascale HPC system that will be deployed at the U.S. Department of Energy’s (DOE) Argonne National Laboratory
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Jul 20, 2022
#ScientificWednesday

Radiative pulsed L-mode operation in ARC-class reactors - fresh one from @CFS_energy and @MIT_Fusion Image
Enhanced confinement & internal transport barriers create large pressure gradients providing significant bootstrap current fractions. High confinement time allows minimization of plasma current improving stability while also reducing external current drive requirements needed
Recently, high temperature superconductor (HTS) technology has dramatically increased achievable on-axis magnetic field in reactor designs. Since fusion power density scales, this technological advancement provides opportunities to improve self-consistent reactor scenarios
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