How Partial Pressure Measurement Supports Plasma Diagnostics in Nuclear Fusion Research

A mass spectrometer converts a gas’s partial pressure (P) into an electrical signal current (I). Its sensitivity (S) describes how strongly the instrument responds, and is defined by the relationship S = I / P.

Using this value, pressure can be computed from the signal current measurement using the formula P_a = I_a / S_a, where ‘a’ represents the gas species.

The mass spectrometer typically operates in Zone 1 (‘Z1’), where the peak width is 1 amu, as seen in Figure 2. If the current is measured at mass m, and only a single species a is present at that mass, then I_m^Z1 = I_a^Z1.

Combining the equations results in P_a^Z1 = I_m^Z1 / S_a^Z1, simplifying the calculation of the pressure of species ‘a’.

If two gas species possess an identical nominal mass ‘m’, then I_m^Z1 = I_a^Z1 + I_b^Z1. Where this is true, it is not possible to determine the individual currents or the partial pressures of ‘a’ and ‘b’.

Dual Zone Instruments

Mass spectrometers can also function in Zone H (‘ZH’), which offers significantly greater resolving power. This allows for the separation of species ‘a’ and ‘b’, which share identical nominal mass, even with an actual mass separation value as low as 0.005 amu. Each signal current is measured as I_a^ZH and I_b^ZH, as shown in Figure 1.

Define the ratio of signal currents as Q = I_a^ZH / I_b^ZH

Given that the Sensitivity Ratios in Z1 and ZH are equivalent, i.e., S_a^Z1 / S_b^Z1 = S_a^ZH / Sb^ZH, and as S = I / P and P is constant, it follows that,

I_a^Z1 / I_b^Z1 = Q

Therefore, I_a^Z1 = Q * I_b^Z1

Assessing the sensitivity in ZH mode is challenging. For this reason, pressures are best calculated using the signal current measured in Z1 mode, where the species sensitivity is generally known or can be readily quantified as needed.

Given that I_m^Z1 = I_a^Z1 + I_b^Z1

then I_m^Z1 = Q*I_b^Z1 + I_b^Z1

it follows that I_m^Z1 = I_b^Z1 * (1 + Q)

hence I_b^Z1 = I_m^Z1 / (1 + Q)

and I_a^Z1 = I_m^Z1 / (1 + 1/Q)

Now, the individual pressures for both species can easily be calculated,

P_a = I_a^Z1 / S_a^Z1 or P_a = (I_m^Z1 / (1 + 1/Q)) / S_a^Z1 or P_a = I_m^Z1 / ((1 + (I_b^ZH / I_a^ZH)) * S_a^Z1 )
P_b = I_b^Z1 / S_b^Z1 or P_b = (I_m^Z1 / (1 + Q)) / S_b^Z1 or P_b = I_m^Z1 / ((1 + (I_a^ZH / I_b^ZH)) * S_b^Z

Figure 1. Image Credit: Hiden Analytical

Figure 2. Image Credit: Hiden Analytical

Example: He and D₂ Partial Pressure Determination Using DLS-2

This shows how Massoft displays the instantaneous computation of He and D₂ partial pressures and He concentration.

Image Credit: Hiden Analytical

Image Credit: Hiden Analytical

Overlapping Species Compatible with Measurement by Dual Zone Instruments

Source: Hiden Analytical 

This information has been sourced, reviewed, and adapted from materials provided by Hiden Analytical.

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