4.2 Langmuir Probe Measurements

Langmuir probes are essential tools for measuring plasma parameters. By inserting a small electrode into the plasma and analyzing the resulting current-voltage curve, scientists can determine electron temperature, plasma potential, and electron density.

These probes come in single, double, and triple configurations, each with unique advantages. However, they have limitations, including plasma perturbation and magnetic field effects, which researchers must consider when interpreting results.

Langmuir Probe Measurements in Plasma Diagnostics

Langmuir probe working principles

Top images from around the web for Langmuir probe working principles

• 

  Analysis of Langmuir Probe Characteristics for Measurement of Plasma Parameters in RF Discharge ... View original

  Is this image relevant?

• 

  Theoretical Study of Spherical Langmuir Probe in Maxwellian Plasma View original

  Is this image relevant?

• 

  Analysis of Langmuir Probe Characteristics for Measurement of Plasma Parameters in RF Discharge ... View original

  Is this image relevant?

• 

  Analysis of Langmuir Probe Characteristics for Measurement of Plasma Parameters in RF Discharge ... View original

  Is this image relevant?

• 

  Theoretical Study of Spherical Langmuir Probe in Maxwellian Plasma View original

  Is this image relevant?

1 of 3

Top images from around the web for Langmuir probe working principles

• 

  Analysis of Langmuir Probe Characteristics for Measurement of Plasma Parameters in RF Discharge ... View original

  Is this image relevant?

• 

  Theoretical Study of Spherical Langmuir Probe in Maxwellian Plasma View original

  Is this image relevant?

• 

  Analysis of Langmuir Probe Characteristics for Measurement of Plasma Parameters in RF Discharge ... View original

  Is this image relevant?

• 

  Analysis of Langmuir Probe Characteristics for Measurement of Plasma Parameters in RF Discharge ... View original

  Is this image relevant?

• 

  Theoretical Study of Spherical Langmuir Probe in Maxwellian Plasma View original

  Is this image relevant?

1 of 3

• Langmuir probes measure local plasma parameters by inserting a small electrode into the plasma (thin wire, small disk)
• Probe is biased with a variable voltage and the resulting current is measured
• Current-voltage (I-V) characteristic curve obtained from probe measurements provides information about plasma parameters
• I-V curve divided into three regions:
  • Ion saturation region: highly negative voltages, probe attracts only ions
  • Electron retardation region: voltages below plasma potential, probe attracts both ions and electrons, electron current partially repelled
  • Electron saturation region: voltages above plasma potential, probe attracts both ions and electrons, electron current dominates

Derivation of plasma parameters

• Electron temperature ($T_e$) derived from slope of electron retardation region in semi-log plot of I-V curve
  • Slope equal to $e/(k_B T_e)$, where $e$ is elementary charge and $k_B$ is Boltzmann constant
• Plasma potential ($V_p$) is voltage at which probe current changes from electron retardation region to electron saturation region
  • Determined by finding knee point in I-V curve or maximum of first derivative of I-V curve
• Electron density ($n_e$) calculated using electron saturation current ($I_{es}$) and probe area ($A_p$)
  • $n_e = I_{es} / (e A_p \sqrt{k_B T_e / (2 \pi m_e)})$, where $m_e$ is electron mass

Types of Langmuir probes

• Single Langmuir probe: single electrode inserted into plasma, biased with variable voltage, resulting current measured
• Double Langmuir probe: two identical electrodes, biased with fixed voltage difference between them
  • Eliminates need for reference electrode and reduces perturbation to plasma
  • Provides floating potential measurement and allows for faster sweeping of probe voltage
• Triple Langmuir probe: three electrodes, fixed voltage difference between two, floating third electrode
  • Allows for instantaneous measurements of plasma parameters without voltage sweeping
  • Useful for measuring rapidly changing plasmas or spatial mapping of plasma parameters

Limitations of Langmuir measurements

• Plasma perturbation: inserting probe can disturb local plasma properties, affecting measurements
  • Probe size should be minimized to reduce perturbation
• Magnetic field effects: strong magnetic field can affect probe measurements by altering electron and ion trajectories
  • Corrections may be needed to account for magnetic field effects (magnetized probe theory)
• Sheath effects: sheath formation around probe can affect current collection and lead to deviations from ideal I-V characteristic
  • Sheath expansion and contraction during voltage sweeping can introduce errors
  • Corrections (Allen-Boyd-Reynolds (ABR) theory) can be applied to account for sheath effects
• Secondary electron emission: high-energy electrons or ions striking probe surface can cause secondary electron emission, affecting measured current
  • Effect more pronounced in high-temperature plasmas, can lead to overestimation of electron current
• Probe contamination: exposure to plasma can cause probe surface to become contaminated or sputtered, altering electrical properties and affecting measurements
  • Regular cleaning or replacement of probe may be necessary to maintain accurate measurements