A Faraday cup is a
metal (conductive) cup designed to catch
charged particle
In physics, a charged particle is a particle with an electric charge. It may be an ion, such as a molecule or atom with a surplus or deficit of electrons relative to protons. It can also be an electron or a proton, or another elementary pa ...
s in
vacuum. The resulting current can be measured and used to determine the number of
ions or
electrons hitting the cup.
The Faraday cup was named after
Michael Faraday who first theorized ions around 1830.
Examples of devices which use Faraday cups include
space probe
A space probe is an artificial satellite that travels through space to collect scientific data. A space probe may orbit Earth; approach the Moon; travel through interplanetary space; flyby, orbit, or land or fly on other planetary bodies; or ...
s (
Voyager 1, &
2,
Parker Solar Probe
The Parker Solar Probe (PSP; previously Solar Probe, Solar Probe Plus or Solar Probe+) is a NASA space probe launched in 2018 with the mission of making observations of the outer corona of the Sun. It will approach to within 9.86 solar radii ...
, etc.) and
mass spectrometers.
Principle of operation
When a beam or packet of
ions hits the metallic body of the cup, the apparatus gains a small net charge while the ions are neutralized as the charge is transferred to the metal walls. The metal part can then be discharged to measure a small current proportional to the number of impinging ions. The Faraday cup is essentially part of a
circuit where ions are the charge carriers in vacuum and it is the interface to the solid metal where electrons act as the
charge carriers (as in most circuits). By measuring the
electric current (the number of electrons flowing through the circuit per second) in the metal part of the circuit, the number of charges being carried by the ions in the vacuum part of the circuit can be determined. For a continuous beam of ions (each with a single charge), the total number of ions hitting the cup per unit time is
:
where N is the number of ions observed in a time t (in seconds), I is the measured current (in
amperes) and e is the
elementary charge (about 1.60 × 10
−19 C). Thus, a measured current of one nanoamp (10
−9 A) corresponds to about 6 billion ions striking the Faraday cup each second.
Similarly, a Faraday cup can act as a collector for electrons in a vacuum (e.g. from an
electron beam). In this case, electrons simply hit the metal plate/cup and a current is produced. Faraday cups are not as sensitive as
electron multiplier detectors, but are highly regarded for accuracy because of the direct relation between the measured current and number of ions.
In plasma diagnostics
The Faraday cup utilizes a physical principle according to which the electrical charges delivered to the inner surface of a hollow conductor are redistributed around its outer surface due to mutual self-repelling of charges of the same sign – a phenomenon discovered by
Faraday
Michael Faraday (; 22 September 1791 – 25 August 1867) was an English scientist who contributed to the study of electromagnetism and electrochemistry. His main discoveries include the principles underlying electromagnetic induction, ...
.
The conventional Faraday cup is applied for measurements of ion (or electron) flows from plasma boundaries and comprises a metallic cylindrical receiver-cup – 1 (Fig. 1) closed with, and insulated from, a washer-type metallic electron-suppressor lid – 2 provided with the round axial through enter-hollow of an aperture with a surface area
. Both the receiver cup and the electron-suppressor lid are enveloped in, and insulated from, a grounded cylindrical shield – 3 having an axial round hole coinciding with the hole in the electron-suppressor lid – 2. The electron-suppressor lid is connected by 50 Ω RF cable with the source
of variable DC voltage
. The receiver-cup is connected by 50 Ω RF cable through the load resistor
with a sweep generator producing saw-type pulses
. Electric capacity
is formed of the capacity of the receiver-cup – 1 to the grounded shield – 3 and the capacity of the RF cable. The signal from
enables an observer to acquire an
I-V characteristic of the Faraday cup by oscilloscope. Proper operating conditions:
(due to possible potential sag) and
, where
is the ion free path. Signal from
is the Faraday cup
I-V characteristic which can be observed and memorized by oscilloscope
In Fig. 1: 1 – cup-receiver, metal (stainless steel). 2 – electron-suppressor lid, metal (stainless steel). 3 – grounded shield, metal (stainless steel). 4 – insulator (teflon, ceramic).
– capacity of Faraday cup.
– load resistor.
Thus we measure the sum
of the electric currents through the load resistor
:
(Faraday cup current) plus the current
induced through the capacitor
by the saw-type voltage
of the sweep-generator: The current component
can be measured at the absence of the ion flow and can be subtracted further from the total current
measured with plasma to obtain the actual Faraday cup
I-V characteristic for processing. All of the Faraday cup elements and their assembly that interact with plasma are fabricated usually of temperature-resistant materials (often these are stainless steel and teflon or ceramic for insulators). For processing of the Faraday cup
I-V characteristic, we are going to assume that the Faraday cup is installed far enough away from an investigated plasma source where the flow of ions could be considered as the flow of particles with parallel velocities directed exactly along the Faraday cup axis. In this case, the elementary particle current
corresponding to the ion density differential
in the range of velocities between
and
of ions flowing in through operating aperture
of the electron-suppressor can be written in the form
where
is elementary charge,
is the ion charge state, and
is the one-dimensional ion velocity distribution function. Therefore, the ion current at the ion-decelerating voltage
of the Faraday cup can be calculated by integrating Eq. () after substituting Eq. (),
where the lower integration limit is defined from the equation
where
is the velocity of the ion stopped by the decelerating potential
, and
is the ion mass. Thus Eq. () represents the
I-V characteristic of the Faraday cup. Differentiating Eq. () with respect to
, one can obtain the relation
where the value
is an invariable constant for each measurement. Therefore, the average velocity
of ions arriving into the Faraday cup and their average energy
can be calculated (under the assumption that we operate with a single type of ion) by the expressions
where
is the ion mass in atomic units. The ion concentration
in the ion flow at the Faraday cup vicinity can be calculated by the formula
which follows from Eq. () at
,
and from the conventional condition for distribution function normalizing
Fig. 2 illustrates the
I-V characteristic and its first derivative
of the Faraday cup with
installed at output of the
Inductively coupled plasma
An inductively coupled plasma (ICP) or transformer coupled plasma (TCP) is a type of plasma source in which the energy is supplied by electric currents which are produced by electromagnetic induction, that is, by time-varying magnetic fields.
Ope ...
source powered with RF
13.56 MHz and operating at 6 mTorr of H2. The value of the electron-suppressor voltage (accelerating the ions) was set experimentally at
, near the point of suppression of the
secondary electron emission
In particle physics, secondary emission is a phenomenon where primary incident particles of sufficient energy, when hitting a surface or passing through some material, induce the emission of secondary particles. The term often refers to the em ...
from the inner surface of the Faraday cup.
Error sources
The counting of charges collected per unit time is impacted by two error sources: 1) the emission of low-energy
secondary electrons from the surface struck by the incident charge and 2)
backscattering
In physics, backscatter (or backscattering) is the reflection of waves, particles, or signals back to the direction from which they came. It is usually a diffuse reflection due to scattering, as opposed to specular reflection as from a mirror, a ...
(~180 degree scattering) of the incident particle, which causes it to leave the collecting surface, at least temporarily. Especially with electrons, it is fundamentally impossible to distinguish between a fresh new incident electron and one that has been backscattered or even a fast secondary electron.
See also
*
Nanocoulombmeter
A Coulombmeter is a tool for measuring the electrostatic charge of a material. A Coulombmeter is used in combination with a Faraday cup or a metal probe
for taking charge measures of a material.
A Nanocoulombmeter is a Coulombmeter that is ca ...
*
Electron multiplier
*
Microchannel plate detector
*
Daly detector
*
Faraday cup electrometer
*
Faraday cage
*
Faraday constant
In physical chemistry, the Faraday constant, denoted by the symbol and sometimes stylized as ℱ, is the electric charge per mole of elementary charges. It is named after the English scientist Michael Faraday. Since the 2019 redefinition of ...
*
SWEAP
SWEAP (Solar Wind Electrons Alphas and Protons) is an instrument on the unmanned space probe to the Sun, the Parker Solar Probe. The spacecraft with SWEAP on board was launched by a Delta IV Heavy on 12 August 2018 from Cape Canaveral, Florida. ...
References
External links
''Detecting Ions in Mass Spectrometers with the Faraday Cup'' By Kenneth L. Busch
{{DEFAULTSORT:Faraday Cup
Mass spectrometry
Measuring instruments
Plasma physics
Plasma diagnostics