CHAPTER 4: POWER BALANCE COMPONENTS & ANALYSIS METHODS
4.4. Region Efficiency Analysis
a larger cross-section [99]. However, it is more sensitive to changes in electron density [99].
In comparison to EIR, MAR involves vibrationally-excited (neutral) molecules150, which interact with either plasma electrons or ions to become temporarily charged and then recombine [i.e. 110, 99]. MAR becomes more dominant at slightly higher plasma temperatures (1 eV < Te < 3 eV) [i.e. 99]. The MAR process has two steps, with two different possible paths, depending on whether an ion or an electron is involved during the first interaction with the neutral gas molecule [i.e. 99]. When the first interaction involves an electron, the first step that occurs is called electron capture dissociation and the second is charge exchange recombination [99]. When the first collision involves an ion, the first step that occurs is a molecular charge exchange and the second is an electron capture dissociative recombination [99]. Figure 4.2 provides a list of the two possible two-step processes assuming the molecular involved is H2 [99].
It is important to note that MAR does not always produce atoms in an excited state and therefore has no spectroscopic signature from photon emission, unlike EIR, which emits photons during radiative recombination processes [99].
4.2.4 Limiting surfaces
Plasma limits on the machine when the magnetic field flux lines intersect with the machine surfaces. Figure 4.3 provides a diagram of the magnetic flux tube lines on Proto-MPEX for a ‘modified flat’ magnetic field configuration.151 The red and blue lines represent the outermost flux line (OFL) and flux lines, respectively. The green box highlights the area where the magnetic field lines may intersect the skimmer machine surfaces. The target and dump plate locations are also shown.
4.3. Deposited Power
The final component of the power balance is the deposited power; that is, the heat flux directly impinging on the end plates 152. The goal of PMI studies in a linear fusion device like Proto-MPEX is to maximize the heat flux and overall power impinging on the target plate. Thus, the intended PFCs are the end plates, specifically the target plate.
Depending on the layout of the fusion device, the magnitude of the heat fluxes can be directly measured from the front of the end plates or interpreted from the heat fluxes measured from the back.153
4.4. Region Efficiency Analysis
To perform the power balance, the Proto-MPEX machine is broken down into three main regions: (1) the helicon region, which includes the area with the helicon antenna, bounded by the nearest diagnostic ports (2.5 and 4.5, z = 1.0 and 1.5 m, respectively);
(2) the upstream region, which extends from the dump plate to the upstream edge of the
150 These molecules are generally the same species as the fuel gas [107].
151 Magnetic coils 1, 6-12 are set to 4500 A, coils 3-4 are set to 160 A, coil 2 is set to 600 A and coil 5 is off.
152 For the purposes of this document, particle recycling off of PFCs is ignored.
153 These measurements are often obtained through IR thermography on Proto-MPEX.
45 helicon region; and (3) the downstream region, which extends from the downstream edge of the helicon region to the target plate. Each of these three regions are broken down into smaller sub-regions to better evaluate plasma transport and losses between diagnostic ports available for data acquisition. The plasma power transport efficiency can be determined in each sub-region to highlight potential areas of the machine with lower efficiency. The division sub-regions also can accommodate the application of multiple power sources with different installation locations. Figure 4.4 provides diagrams of Proto-MPEX partitioned into its three main regions and its sub-regions.
The helicon region is divided into three sub-regions: the helicon antenna, the
downstream edge of the helicon window and the upstream edge of the helicon window.
The upstream region is divided into two sub-regions: from diagnostic port 2.5 to diagnostic port 1.5 and from diagnostic port 1.5 to the dump plate. The downstream region is divided into five sub-regions: from diagnostic port 4.5 to 6.5, from diagnostic port 6.5 to 9.5, from diagnostic port 9.5 to 10.5, from diagnostic port 10.5 to 11.5, and from diagnostic port 11.5 to the target plate.
The amount of power entering the sub-region equals the power exiting the sub-region.
The balance of power entering and exiting the sub-region can be approximated using equation 4.4.
P
enter+ P
source= P
exit+ P
loss (4.4) where Penter is the amount of power entering the region from the previoussub-region, Psource is the power entering the sub-region from an applied power source, such as the helicon, Pexit is the amount of power leaving the sub-region, continuing towards its respective end plate, and Ploss power lost from the main plasma due to different loss mechanisms, such as charge exchange processes.
The efficiency of each sub-region can be evaluated using the following equation:
η =
PexitPenter+Psource
(4.5) where is the efficiency of the sub-region.
4.5. Summary
As previously stated, power accounting helps identify areas for improvement with respect to machine operations by quantifying plasma loss locations and mechanisms.
The power balance is separated into three main components: input power (Pin), lost power (Ploss), and deposited power (Pdep). For this thesis, the helicon is the only power source. The input power is the net (helicon) power after reflected and resistive power losses are subtracted from the nominal injected power. The lost power refers to the power lost from the plasma as the plasma travels from the power source to the end plates. Sources of power losses include radiative transport losses and non-radiative transport losses, such as recombination, elastic collisions, and charge exchange [i.e.
46 11, 99] and limiting surfaces. Deposited power refers to the power that is deposited on the end plates. To perform the power balance, the Proto-MPEX machine is broken down into three main regions: (1) the helicon region; (2) the upstream region; and (3) the downstream region. Each of these three regions are broken down into smaller sub-regions to better evaluate plasma transport and losses between diagnostic ports
available for data acquisition. The plasma power transport efficiency can be determined in each sub-region to highlight potential areas of the machine with lower efficiency.
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