Emission of electrons in a vacuum to create an electric current

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Emptiness is how the word vacuum is translated from Latin. Vacuum is usually called a space in which there is gas, the pressure of which is hundreds, and maybe thousands of times lower than atmospheric pressure. On our planet, a vacuum is created artificially, since such a state is impossible under natural conditions.

Types of vacuum

How does electric current behave in a vacuum? Like any current, a current in a vacuum appears in the presence of a source with free charged particles.

What particles create an electric current in a vacuum? To create a vacuum in any closed vessel, it is necessary to pump out the gas from it. This is most often done using a vacuum pump. This is a device that is necessary to pump out gas or steam to the pressure required for the experiment.

There are four types of vacuum: low vacuum, medium vacuum, high vacuum and ultra-high vacuum.

Rice. 1. Vacuum characteristics

Vacuum diode

One of the typical devices using the conductivity of airless space is a vacuum two-electrode electron tube. If a reverse voltage is applied to its positive terminal, then all the electrons emitted by the cathode are returned. With forward bias, charge carriers rush towards the anode. In other words, the alternating signal is rectified. The device works like a diode.

You can study the appearance of electric current in a vacuum and gases using a radio element consisting of the following parts:

• sealed flask;
• metal electrode (anode);
• tungsten spiral (cathode);
• rheostat.

The tungsten filament is in a sealed flask and connected through a rheostat to a generator to regulate the current. The electrode is connected to a microammeter. From it, the circuit, passing through the ballast resistor, closes at the cathode.

The rheostat can be used to regulate the temperature of the cathode. Variable resistance sets the potential difference between the positive and negative terminals. The current-voltage characteristic, that is, the dependence of the anode current on voltage, will be formed as follows. Let's say there is no voltage. Then the electrons emitted from the cathode will be attracted back. No current flows in the anode circuit. If a negative signal is applied to the pin, the electrons will be repelled. No current flows again.

When a positive voltage is applied to the anode, an electric field is created. It creates a force directed towards the anode. The speed of flight of electrons is different, since some of them are repelled by previously emitted particles. The greater the field strength, the stronger the current will begin to flow. But the change will not occur linearly. For example, if the voltage is doubled, the number of electrons emitted from the cathode will increase by more times than this number. The greater the potential difference, the less the space charge of the electrons.

On the graph, this dependence will represent a semi-cubic parabola. It can be described by an approximate formula: I = U3/2. If you continue to increase the voltage, the tension becomes much greater than the field created by the spatial cloud. All electrons will begin to reach the anode. The current strength will no longer depend on the voltage. This is represented by a straight line on the current-voltage characteristic, and the effect is called saturation current.

Electric current in a vacuum

Current in a vacuum cannot exist independently, since vacuum is a dielectric. In this case, a current can be created using thermionic emission. Thermionic emission is a phenomenon in which electrons escape from metals when heated. Such electrons are called thermionic electrons, and the entire body is an emitter.

This phenomenon was first noticed by the American scientist Thomas Edison in 1879.

Rice. 2. Thermionic emission

Emission is divided into:

• secondary electron (knocking out by fast electrons);
• thermionic (evaporation of electrons from a hot cathode);
• photoelectronic (electrons are knocked out by light);
• electronic (knocking out with a strong field).

Electrons will be able to fly out of the metal if they have sufficient kinetic energy. It must be greater than the electron work function for a given metal. Electrons escaping from the cathode form an electron cloud. Half of them return to their original position. In the equilibrium state, the number of electrons emitted is equal to the number of electrons returned. The density of the electron cloud depends directly on the temperature (i.e., as the temperature rises, the density of the cloud becomes greater).

When the electrodes are connected to a source, an electric field arises between them. If the positive pole of the current source is connected to the anode (cold electrode), and the negative pole to the cathode (heated electrode), then the electric field strength will be directed towards the heated electrode.

Physics of the process

An electric current in a vacuum can only be generated by the directed movement of electrons. It is possible to introduce them by placing them in a metal environment. In order for particles to leave the surface of the conductor, energy must be given to them. This process is called the work function of electrons leaving the substance.

Its value for different materials was established experimentally . Thus, for the most popular substances the work function is equal to:

• tungsten - 4.5 eV;
• cadmium - 2.2 eV;
• zinc - 4.2 eV;
• barium oxide - 1 eV.

That is, in order to extract an electron, you need to impart a certain energy to it. Only then will he be able to fly out from the surface. In the normal state, the energy of an electron in a metal is 3.2 KT (thermal). At room temperature (T = 300 K) KT = 0.026 eV. This value will clearly not be enough for electrical conductivity to appear in a vacuum.

If you heat the body to 3 thousand degrees Kelvin (many metals begin to melt), then KT = 0.26 eV. This value is still not enough to knock out electrons. But in fact, carriers have a certain energy distribution. The found value shows the average value. Therefore, in a body, due to the high density of charged particles, there will definitely be electrons that have an energy exceeding the work function.

An electron cloud appears above the surface of the conductor. Moreover, the higher the temperature, the denser it will be. The emitted electron leads to a change in the charge of the metal. As a result, he begins to retract back. Balance is established. Whatever number of electrons is emitted, the same number returns.

In order for a flow of charges to form, an auxiliary circuit must be introduced. In other words, provide electrons with additional energy. The relationship between current and voltage in the case under consideration will not correspond to Ohm's law. After all, the formed electron cloud delays the newly escaping electrons. But if you increase the voltage at the other terminal, the concentration of carriers in the formed field will decrease, which means that the braking effect will also decrease. This will lead to an increase in current.

Thus, the escaping electrons can be likened to electron rockets that have overcome gravity. If you connect the positive electrode of a current source to the terminal, the resulting electromagnetic field between the spiral and the electrode inside the vacuum flask will direct electrons towards it. Electric current will flow inside.

Problem solving

In school notes and essays you can find tasks related to the appearance of current in a vacuum. These tasks allow high school students to consolidate the material they have covered and understand the practical application of the effect.

Here are three of them, designed for tenth grade students:

1. Explain the reason why the voltage decreases when the current increases during an arc discharge. To confirm the correctness of what has been said, you need to reason like this. As the current increases, thermionic emission from the cathode terminal increases. As a result, the number of charge carriers increases. In turn, this leads to a decrease in the resistance of the area between the electrodes. The decrease in resistance occurs faster compared to the increase in current. That is, in a vacuum the linearity established by Ohm’s law is violated, which means the voltage decreases.
2. What charged particles create a current in a vacuum? Since vacuum is a dielectric, it does not contain particles that could conduct electricity. For current to occur, it is necessary to introduce into the medium additional material capable of emitting charges. When heated, electrons are emitted from the surface. Therefore, only electrons are able to participate in charge transfer.
3. Prove that during an elastic collision of a molecule and an electron, less energy is transferred than during an inelastic collision. Since during a straight-line impact the law of conservation of energy is valid, the following equalities will be true: mV2 / 2 = mV2 e / 2 + mV2m / 2; mV2 = mV2e + mV2m, where m are the masses of the particles, and v are their velocities obtained after the impact. These equations can be reduced to a system and solved for Ve and Vm. The result is an equality: Vм = (2 * m * V) / (me + mm). From this we can draw conclusions:

• The energy received by the molecule will be equal to: W = mV2m / 2 = (mV2 / 2) * ((4 m * m e) / (m e + m))2. Considering that me is significantly less than m, the electron mass can be neglected. Therefore W = (4me * me * V2) / m * 2. It follows from this that a small part of the energy is transferred to the molecule.
• In an inelastic collision, the law of conservation of momentum applies. The electron gives up all its charge: w = mV2 / 2.

Thus, the movement of electrons in a vacuum is essentially a type of electric current. It can only be obtained by placing a heated cathode in the medium. It is this that will be the source of electron emission.

The field that arises between the cathode and the anode will impart speed to the particles and determine their direction.

MOVEMENT OF ELECTRONS IN VACUUM. ELECTRONIC TUBE CATHODES

The electron, discovered at the very end of the last century, is still an object of scientific research, which is discovering more and more of its properties. It has long been established that the electron has a negative charge e =

1.6 • 10-19
to
rest mass
t
= 9 • 10-28
g
1.

Let's imagine the space between two flat plates (electrodes) in an evacuated glass container (Figure 8-1). Let us remember that to evacuate or create a vacuum in a cylinder means to pump out the air from it with special pumps; For the chemical absorption of gases that can be released inside the lamp cylinder during its operation, absorbers (getters) are used, for example barium, which is sprayed inside the cylinder during the manufacture of the lamp and forms a coating on the inner surface of the glass.

Let us further imagine that even before pumping out the cylinder, conductors were connected to the plates, soldered into the glass and serving as leads from the plates to the outside. Outside the cylinder, the positive terminal of the battery is connected to one conductor, and the negative terminal to the other. Then the plate connected to the “plus” becomes called the anode, and the plate connected to the “minus” becomes the cathode.

Let an electron with a negligibly low initial velocity fly out from the surface of the cathode into the balloon. It comes under the influence of an electric field, which is shown in Fig. 8-1 is depicted as lines of force directed from the anode to the cathode. The electron is attracted to the anode with a constant force.

It is easy to calculate this force. If the field between the anode and cathode is considered uniform, then its strength

where d

— distance between electrodes. But the electric field acts on the electron with a force equal (according to Coulomb’s law) to the product of its charge and the field strength, i.e.

F = eE,

and this force is directed towards the field. The electron will begin to move from bottom to top, acquiring acceleration, which, in accordance with Newton's second law, is equal to the ratio of force to mass;

The movement will be uniformly accelerated; therefore, as the electron moves, its speed will increase and, along with it,

1 At high speeds, the mass of the electron increases, however, the speeds that electrons reach in electrovacuum devices are significantly less than the speed of light, and under these conditions the mass of the electron can be considered constant” kinetic energy, which by the end of the journey will acquire a value

where v

— speed at the end of the path
d.
The energy acquired by an electron when moving in an accelerating field is equal to the work expended by the electric field, i.e., ultimately, by the battery. Work is calculated as the product of force and path:

W

=
Fd - eEd = eU.
Equating the energy expended by the field to the energy acquired by the electron, we write the basic equation of motion of an electron in an electric field:

where can we find the speed of the electron at the end of the path?

Knowing that the ratio of the electron charge to its mass under the conditions we have accepted is a constant value, and expressing the speed in practical units (km/sec),

we get:

(8-1)

So, if the voltage between the electrodes U =

100
V,
then the speed of the electron at the end of the journey will be 6,000
km/sec,
which, as we see, is much lower than the speed of light (300,000
km/sec).
It is easy to determine the time of flight of an electron from the cathode to the anode, knowing the distance d

between them.
It is known that the average speed of uniformly accelerated motion is v
cf =
v/2.
Therefore time
t = d/v
cp.
For example, if in the above case d
= 1
cm
(i.e. 10-5
km
), then the time of flight will be
t =
2
d/v
~= 2 • 10-6/6 • 108 = 1/3 • 10- 8
sec,
i.e. approximately 0.003
µsec.
This time turned out to be equal to the period of a radio wave 1 m long
.
So, the field that accelerates the movement of the electron does work that increases the kinetic energy of the electron. When hitting the anode surface, the kinetic energy of the electron is converted into thermal energy: the electron impacts heat the anode.

Let us consider the second case of electron motion in the same balloon. Let us assume that an electron located close to the anode surface received a push towards the cathode. The initial speed of the electron turned out to be directed towards the electric force acting on it. Then the field will turn out to be decelerating rather than accelerating the movement of the electron; the electron will move uniformly slowly. The energy that the electron acquired at the moment of the initial push will be spent when it moves in the braking field: the electron in this case gives up energy to the electric field. The following case is also possible: before reaching the cathode, the electron will expend all its energy, stop, and then begin to move back to the anode, accelerating uniformly.

The third characteristic case is a push imparted to the electron in a direction transverse to the field. The movement will be non-linear: the electron will deviate from the transverse path towards the anode, and the degree of deviation will depend both on the initial speed of the electron and on the strength of the electric field (E

=
U/d).
These are the simplest cases of interaction between an electron and an electric field. The interaction always manifests itself in a change in the speed of the electron and in the exchange of energy between the electron and the field created by the anode battery. In an accelerating field, an electron acquires energy from a battery, and in a decelerating field, it gives energy to the battery. If the electron were moving not in a vacuum, but in a space filled with gas, then the processes we described would be disrupted due to collisions of the electron with gas molecules. The interaction of an electron with a magnetic field will be discussed below.

Now let’s imagine that electrons appear continuously near the cathode and, under the influence of an electric field, move towards the anode. Then an electric current will be established in the vacuum and in the battery circuit, the magnitude of which will be determined by the number of electrons reaching the anode per second. So, if approximately 7 • 1012 electrons fly through the balloon per second, then the current will be 1 μA.

It is still customary to indicate the direction of current in the opposite direction to the direction of electron motion.

You can create conditions for establishing and maintaining current in a vacuum device by choosing a cathode that has the properties of emitting (expelling) electrons from its surface. Such a cathode can be called an “emitter” (sending out electrons); The anode can be called a “collector” (collecting electrons). However, the names “emitter” and “collector” are more often used in semiconductor devices.

In order to create a noticeable current in a vacuum, the effect of voltage alone on the cathode is insufficient, since electrons can freely exit the cathode metal beyond its surface. The fact is that metal atoms from which electrons have been separated become positive ions; they attract into the metal every electron that escapes the surface. Only at a sufficiently high initial escape velocity is the electron able to break away from the metal. The emission of electrons from the cathode surface can increase significantly if additional energy is provided to the electrons in the metal.

There are three practically used methods for increasing the energy of electrons in a conductor: heating, which creates thermionic emission; irradiation of the surface of the conductor with light, creating photoelectron emission; bombardment of the surface of a conductor from the outside with electrons that have high speed and create secondary electron emission. Most types of radio tubes use thermionic emission. The cathode is heated by an electric current, like the filament in an incandescent lamp; This is why electric vacuum devices are called lamps. To heat the cathode there must be an independent current source.

An increase in the temperature of the metal increases the average energy of electron motion throughout the entire mass of the metal, and a significant number of electrons acquire a speed sufficient to escape into the surrounding space. Pure metals produce noticeable emissions only at temperatures of several thousand degrees. Refractory metals, such as tungsten, which is widely used for cathodes of radio tubes, can withstand such heating.

As the simplest example of a radio tube (an electric vacuum device with thermionic emission), consider a diode (a tube with two electrodes) used for rectifying alternating current, detecting and performing other functions in radio equipment.

In a glass evacuated cylinder (Fig. 8-2, a

) two electrodes are strengthened - anode and cathode. The anode in this example is made in the form of a metal cylinder located horizontally and having an outlet upward through the glass. The cylindrical shape is more convenient than the flat one in terms of cathode coverage; but other forms are also possible.

Rice. 8-2. Design and inclusion of a diode.

A

- the simplest diode design;
b -
diode in the circuit?

V

- heat adjustment.

The cathode, in the form of a filament, running along the axis of the cylinder, has two terminals connected to the glow battery. Lamp electrodes are usually designated on diagrams, as shown in Fig. 8-2, b.

Both terminals of the cathode (filament) are connected to an independent incandescent battery B

n
.
The current of this battery passing through the filament heats it to a temperature at which sufficient electron emission is achieved.
If it is necessary to set the precisely specified temperature of the filament, a filament voltmeter V
and a rheostat
R
(in accordance with the diagram in Fig. 8-2,
c).
B is connected between the anode and one of the cathode terminals

and with observance of polarity, ensuring the attraction of electrons to the anode.
The anode current is measured by a mA
connected to the anode circuit;
the magnitude of the current is equal to the sum of the electron charges reaching the anode within a second. The anode current circuit goes from the plus of the anode battery B
a to the anode, then from the anode to the cathode in the evacuated space, then along the cathode to the common point
O
of the batteries and to the minus of battery
B
a (Fig. 8-2,
b).
The direction of the anode current
Ia
is shown opposite to the direction of electron movement.

If we changed the polarity of the anode battery and the anode turned out to be negative in relation to the cathode, then the electric field would not become accelerating, but decelerating, and the movement of electrons to the anode would stop. This makes it possible to use the diode as an AC rectifier.

Let us turn to the design of cathodes. For each metal, including tungsten, at an acceptable temperature a certain (on average) number of electrons per square millimeter is emitted. Consequently, the dimensions of the cathode must be such that the required emission current is obtained from its surface. The greater the anode current we want to obtain, the larger the size of the cathode; Accordingly, more power has to be spent on heating it (a necessary, but not useful, expenditure of power).

Pure tungsten is uneconomical in this regard. It has to be heated to a temperature (at least 2,200° C) at which the metal evaporates and the cathode does not last long (on average up to 1,000 hours).

Only in very powerful lamps can burnt-out tungsten cathodes be replaced, and they find use there.

To reduce the operating temperature of the cathode while maintaining good electron emission, it is necessary to facilitate the release of electrons from the metal. For this purpose, the cathode is coated with a layer of another metal one atom thick. The contact potential difference between the two metals partially compensates for the braking effect of the surface of the base metal and promotes the emission of electrons. Therefore, coating the cathode is called cathode activation.

Among the activating coatings we can mention thorium, which is used to coat the surface of a tungsten filament specially treated with carbon (carbided). Thoriated carbided cathodes have an operating temperature of no higher than 1,700 ° C (yellow heat) and are most often used in lamps for medium-power radio transmitters. A lamp with such a cathode may fail not as a result of filament burnout, but as a result of destruction of the activating coating; in such cases the lamp is said to “lose emission.”

Another activating coating can be oxides of the metals barium or strontium, which are applied not to tungsten, but to nickel. The activating layer of metal is released from the oxides during heat treatment of the cathode. Oxide cathodes operate at temperatures of about 800° C (cherry-red heat). They have a reserve of activating metal in the oxides and therefore are less sensitive to overheating and more durable (5,000 h

and more). In addition, they are capable of producing increased emissions during short-term voltage switching on (pulse operation).

However, all these directly heated cathodes are almost never found in broadcasting receiving and amplifying equipment powered from an alternating current network. The fact is that if a direct filament is fed with alternating current, then the common point O

(see Fig. 8-2,
b)
alternately appears under a positive and negative potential relative to the middle of the filament, and therefore the anode voltage also changes (pulsates), which can create a low-frequency sound (background) in the receiver’s loudspeaker.

Much more widely used in radio and television equipment are lamps with cathodes that are powered by alternating current, but have a constant potential with respect to the anode (equipotential cathodes). The filament in them is not designed to emit; it only heats the cathode separated from it through the insulation. Such cathodes are called heated or indirectly heated cathodes.

Rice. 8-3. Indirect filament cathode device.

A sketch of an indirectly heated cathode (with part of the wall cut out) is shown in Fig. 8-3. The cathode itself is a metal tube 1,

on the surface of which a layer of oxides
2
containing barium is applied.
Inside the tube there is a folded loop of filament 3,
covered with a heat-resistant layer of alundum
4
(an insulating material based on aluminum oxide). There may also be designs of heated cathodes in which the heater is made in the form of a flat spiral, and the cathode is a flat cylinder, closed at one end with an oxidized bottom.

In Fig. 8-4 shows a circuit diagram of a diode with an indirectly heated cathode, and the supply of the filament circuit with alternating current is indicated. Sometimes, in contrast to this pattern, the cathode is connected to one end of the filament; however, the filament circuit and the anode circuit are always separated from one another, that is, they do not have a common area. Therefore, the alternating filament voltage does not affect the anode. At the same time, the massive heated cathode, which has thermal inertia, ensures the constancy of its average temperature with alternating filament current.

Naturally, when the cathode is heated by a filament through the insulation, the efficiency of the filament decreases. When powered from an alternating current network, the issue of filament efficiency is not raised as acutely as when battery-powered portable equipment is used. After switching on, the massive cathodes of “heated” lamps require several seconds to warm up to normal (emission) temperature. In circuits that do not have a cathode-filament connection, it is sometimes necessary to create a voltage between them; this voltage should not exceed hundreds of volts, since at higher values ​​a breakdown of the alundum insulation may occur.

Indirect filament lamps with well-developed production technology have a service life of 5,000 hours or more.

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Thermionic current

Definition 1

If there is an electric field near the surface of a metal, then electrons from the electron cloud form an electric current. This current is called thermionic.

And so, if there are two metal plates in a vacuum, there is a potential difference between them, then a thermionic current will appear between these plates.

The current strength should increase as the potential difference increases. For thermionic current there is a saturation current strength. This is the maximum current at which all the electrons that enter the electron cloud from the cathode surface reach the anode. In this case, there is no reverse current of electrons through the surface into the cathode. The strength of the saturation current does not change with increasing potential difference between the anode and cathode.

For metals, the work function is several electron volts. Moreover, the energy $kT$, even at high temperatures of thousands of kelvins, is only a fraction of an electron - a volt. This means that $\frac{A_v}{kT}=A_v\beta \gg 1,\ \to exp\left[\beta \left(E_k+A_v\right)\right]\gg 1,$ therefore, in the denominator of the formula (4) unity can be neglected and this formula can be written as:

The strength of the saturation current depends on the work function and temperature. For pure metals, significant current can be obtained at temperatures on the order of $2000 K$, which means that metals with high melting points should be used as cathodes. In this case, it is necessary that their work function be minimal. Thus, tungsten, which has a work function of $4.5 eV$, must be heated to a temperature of $2500 K$x.

In order to reduce the operating temperature and reduce the work function, oxide cathodes are used.

Cathode-ray tube

In vacuum tubes, the flow of electrons is directed from the anode to the cathode in all directions. But it is possible to create structures in which the electrons will be directed in one direction. Such a flow is created using special focusing plates. It is often called a cathode ray. It can be used to heat bodies, for example, in vacuum ovens.

By its nature it has the following properties:

• it is affected by an electric and magnetic field (Lorentz force);
• when hitting some substances, for example, zinc sulfide, a focused electron flow leads to an interesting result - glow;
• the beam generates x-rays.

These properties are the basis for a class of vacuum devices called cathode ray tubes (CRTs).

Such a device is arranged as follows. Electrons in the device are generated using thermionic emission. The cathode of the device is a cylinder with a flat base coated with barium oxide. This electrode emits electrons. A grid is used to control their intensity. By applying voltage to it, you can block the flow or unlock it.

The main detail in the definition of an electron flow is its narrow focus. This can be achieved by using additional anode leads. One of them is accelerating, and the other is focusing. Passing through the specified set, an accelerated focused stream flies out of the CRT. The second anode is supplied with positive voltage directly, and the accelerating one through a rheostat. The potential difference is a multiple of tens of kilovolts.

The stream leaving the cannon hits a screen covered with phosphor. This entire system is located in a flask with airless space. In order to move the beam across the surface of the screen, capacitors are used. Depending on the location of their plates, flow deflection occurs. It is caused by voltage applied to the plates. From its value, the beam can be attracted to one side or the other, essentially changing the flow of electric current in a vacuum. This is, in a nutshell, how a CRT works.