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the temperature of the sun
As can be expected from Wien's law and Stefan-Boltzmann's law (see infrared emission) it might be possible to apply such great an amount of energy to matter that its temperature increases to a point were it starts emitting a limited quantity of blue light and even ultraviolet radiation. In the physical processes at the surface of the sun this indeed happens and part of the about four percent contribution of ultraviolet radiation in sunlight is due to this effect.
The measured peak level of the emission spectrum of unfiltered sunlight is located around 500 nanometers, corresponding with the colour green (see electromagnetic spectrum). The reason why we experience the colour of the sun as being yellowish can be found in filtering and scattering by the earth's atmosphere but it is also caused by the
relatively great sensitivity of our eyes for yellow light. From Wien's displacement law it can be calculated that a wavelength of 500 nm corresponds with an effective temperature of about 5800K. In an ordinary incandescent lamp the temperature stays limited to about 2800K and the ultraviolet component in its electromagnetic spectrum is no higher than only a few tenths of a percent.
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The preceding paragraphs did not fully consider the influence of gas pressure, temperature and field intensity on the processes in the discharge tube. These physical units however, are of crucial importance for the nature- and the effectiveness of a gas discharge. When the gas pressure is too low there are not enough gas atoms or -molecules available to produce a significant quantity of ultraviolet radiation or to start a discharge at all. When on the other hand the gas pressure is too high, free electrons are not able to gain enough speed before they collide with an atom and as a result mainly elastic collisions will occur. An important property in this context is the mean free path L that indicates the average distance an electron can travel in the longitudinal direction of an electric field without a collision with a gas atom. For example: The ionisation energy of mercury is about 10 eV. The average field intensity F is the potential difference UL between the cathode and the anode, divided by the distance d between cathode and anode. With UL=500 volt and d=2 cm, F equals 500/0,02 = 25.000 V/m. To allow an electron to ionise an atom of mercury, a mean free path L of (10 V)/(25.000 V/m) or 0,4 mm would than be required. Measured on the scale of an atom this is a long distance that can only be realised in an atmosphere that contains a low quantity of atoms so at a low gas pressure. In practice the circumstances are a little better since the voltage drop between the cathode and the anode is not linear. The largest drop in voltage is located just after the cathode in an area that measures only one or a few millimeters. This is the area where the majority of the ionisations take place and from here most ions travel towards the cathode to free additional electrons. In a quiet glow discharge a specific light effect may be noticed in this ionisation area, caused by recombinations between electrons that just left their energy in their firsts collision and atoms that just have been ionised and did not speed up in the direction of the cathode yet. In an arc discharge this phenomena disappears in the violence of the thermal emission of the cathode. In the area after the first ionisation zone and just before the anode, the voltage drops only little and the field intensity is just enough to form a column of hot gas (plasma) in which in a delicate equilibrium a continuous process of ionisation takes place. Finally it is this column that is responsible for the emission of the desired ultraviolet radiation.
temperature and gas pressure
Under low-pressure conditions the ionisations within the gas column are mainly caused by collisions of free electrons with gas atoms. The temperature of these free electrons can be very high but since the mass of an atom is much greater than that of an electron and because only a limited part of the atoms will get ionised, the mean gas temperature will rise only a little. An example of such a low-pressure gas discharge can be found in sun-
lamps of the Cooper-Hewitt type in which the cathode consists of a relatively large pool of mercury in a vacuum tube. The arc discharge is established between the anode and a hot spot at the surface of the cathode pool. The mercury vaporises at the hot spot and condenses in the cooler anode part of the tube from were it flows back into the pool of mercury. Because of
the temperature dependency of the gas pressure a proper cooling of the tube is essential for keeping the pressure low. The electric current is limited to such a level that only a part of the mercury will vaporise. Since the atmosphere within the gas discharge tube will become saturated with mercury vapour, this type of ultraviolet radiator is often determinated as a saturation lamp. By lamps that operate at higher gas pressures the number of ionisations would decrease due to the shortening of the mean free path when no other measures were taken. To avoid this, the decrease in ionisations has to be compensated by an increase of the supply voltage (and by consequence also the field intensity) to a level where the required ionisation voltage is reached again within the shortened free path. Due to the increased gas pressure the number and intensity of the collisions will now increase, causing an increase of the gas temperature too. Because the gas pressure p is proportional to the absolute temperature T according the relation p=nkT (in which n is the number of gas atoms and k is Boltzmann's factor) pressure and temperature will rise until a new thermal equilibrium is reached. At higher temperatures the majority of the ionisations is caused by thermal emission of electrons within the plasma column. The additional produced electrons limit the need to increase the field intensity fully proportionally to the increase of the gas pressure. With gas discharges in an environment saturated with mercury vapour and under low-pressure conditions the process of ionisation takes place over the entire crosscut of the tube. At higher pressures this process is more and more located in the centre of the cross-cut, leaving a thermal isolating vacuum between the electrical arc and the wall of the
tube. This isolation allows the temperature of the electrical arc to rise as high as 6000 ºC, much higher than the melting point of the tube. In a high-pressure gas discharge tube the amount of mercury is limited to no more than a few hundred milligrams and due to the high temperatures in the tube all the mercury will vaporise rapidly.
An increase of the supply voltage once a dark discharge had been established, will intensify the electric field. As a consequence the free electrons will travel towards the anode at an ever-increasing speed, making them to collide more and more violently with the gas atoms they meet on their path. In point B of the voltage-current characteristic the majority of the collisions is still of the elastic type but from point C on, more and more electrons within the atoms will get excited. Finally some of the involved atoms will even get ionised, producing additional electrons to participate in the charge displacement towards the anode. Once these secondary electrons are able to pick up so much energy from the electric field that they are able to free another electron by themselves, small avalanches of electrons eventually might occur. The number of these irregular, individual avalanches per unit of time is proportional to the strength of the background radiation and it is this type of discharge that is used in Geiger-Müller tubes to detect radioactivity. A secondary effect from the electron avalanches are clouds of ionised atoms that, due to their net positive charge, will be attracted towards the cathode and finally will collide with it. A part of these collisions may be so violent that they have enough energy to free even more electrons out of the cathode. These electrons will join the electrons already freed by the background radiation and in the avalanches and they will travel towards the anode as well. Due to these additional electrons the number and intensity of the individual avalanches increases and at point D in the characteristic the number of electrons that is freed from the cathode finally turns out to be sufficient to maintain a continuous avalanche, independent of the intensity of the background radiation. The path between cathode and anode now becomes conductive and the voltage over the discharge tube will steeply drop to E. The breakdown voltage D at which the path becomes conductive is called the spark voltage. Due to the serial resistor, the current through and the voltage over the discharge tube will stabilise in D' and the dark discharge has now transformed into a so-called glow discharge. A glow discharge is characterised by a low current, a high voltage and a relatively calm discharge process. The temperature of the cathode will hardly rise under the quiet but continuous bombardment with ions which free just enough electrons to keep the glow discharge going on. Due to this behaviour the glow discharge is also known as cold-cathode emission and it is this type of discharge that is used in the bent
glass tubes that form the well known coloured neon signs that decorate our cities, an application introduced by Georges Claude in 1911. A glow discharge is also used in some
types of sun-lamps. A tube of quartz glass is filled with mercury vapour and the serial ballast is dimensioned in such a way that it limits the current through the tube to the level of a glow discharge. For a glow discharge the output of ultraviolet radiation measured per meter tube is relatively low, compared with the output of an arc discharge. Partly this is
compensated by the use of relatively long tubes. A special kind of glow discharge can be found in sun-lamps from Sun-Kraft. This company used discharge tubes without electrodes. The ionisation of the mercury vapour was obtained by placing the tube in an electric field, generated by a high frequency oscillator, a concept already shown by Nikola Tesla in 1893. Due to the lack of electrodes the lifetime of these tubes was virtually unlimited as long as they were not damaged mechanically. Glow discharges also play a
major role in the automatic start circuits of Tube-Lights (see electrical circuits) who are, apart from traditional lighting purposes, also applied frequently in face-tanners and in armatures for light therapies.
A next increase of the supply voltage once a glow discharge had been established, further intensifies the electric field. This causes the collisions of electrons with gas atoms or the anode and between gas ions and the cathode to become more and more violent. This in turn increases the temperature of the gas and the electrodes and finally, under the lasting bombardment of gas ions, isolated hot spots will develop on the cathode. This is around point G of the voltage-current characteristic. In a process similar to what happens in the glowing filament of an incandescent lamp, the hot spots at the cathode will start to emit electrons by thermal emission. In an incandescent lamp this thermal emission is not desired and will be prevented as much as possible. In a gas discharge tube however, the existence of some local glowing of the cathode is a crucial condition to start an arc discharge. Around a glowing hot spot a cloud of negatively charged electrons will emerge. This cloud of electrons will attract positively charged ions that result from the glow discharge. A part of these ions will recombine with the electrons around the cathode but most of them will collide upon the cathode and hence increase the intensity of the hot spot even further. Again a chain reaction will develop and in a fraction of a second the whole cathode will start glowing. From point G of the characteristic on, the relatively calm glow discharge
transforms into a much more violent arc discharge. An arc discharge is characterised by a high electric current, a low voltage across the discharge tube and a much more violent discharge process compared with that of a glow discharge. Another characteristic is the thermal electron emission of the cathode. The arc discharge derived its name from the
current through the circuit, causing the voltage over the discharge tube to drop even further. In point G'' the voltage drop in reaction to an increase in current has become small enough to allow the resistor to compensate fully for the drop of voltage over the tube. Nevertheless the current keeps rising because the sum of the voltage over the tube and over the resistor is still lower than the supply voltage U. Only in point G' the balance is restored and from here on the increase in voltage over the resistor due to an increase in current exceeds the drop of the voltage over the discharge tube. A further increase of current is now prevented and current and voltage will stabilise in G'. What can not be read from the characteristic is that the nature of the arc discharge is also influenced by temperature. At higher temperatures more electrons will be freed, resulting in more and more violent collisions which in turn free more electrons. Due to this process it can take one or even a few minutes before the behaviour of the arc discharge stabilises at a constant working temperature. To prevent the arc discharge from falling back into a glow discharge under the fluctuation of external conditions, the supply voltage has to be increased until point H of the characteristic. The sun-lamp finally fulfils its task.
phenomena that under atmospheric conditions a continuous and horizontal voltaic arc between two carbon rods will bend upwards under the influence of the upwards flowing hot air around it. The working point of the electric current and voltage will stabilise in
point G' and the underlying mechanism is illustrated in the figure next to here. Starting in point G of the characteristic a small increase in current will cause a more than proportional drop in the voltage over the discharge tube. Due to the increased current the voltage over the resistor will increase as well but not enough to compensate for the drop in voltage over the tube. The voltage source U will try to compensate for the potential difference by raising the
Under certain circumstances a gas discharge can be a much more effective way to generate ultraviolet radiation than heating up a solid. In principle a gas discharge can be obtained by generating a potential difference between two conductors (electrodes) that are separated from each other by air or another gaseous medium. A sufficiently high potential difference may cause a continuous voltaic arc between the electrodes, accompanied by a strong electromagnetic radiation. From itself such electromagnetic radiation may already contain a significant high quantity of ultraviolet radiation and by choosing the proper composition for the medium and the electrodes this amount of ultraviolet radiation can be increased even further. Although an electric gas discharge in its natural form as lightning is older than humanity, the mechanisms behind it were discovered no earlier than the first half of the 19th century. In a gas discharge, a part of the electric charge is transported by electrons in a process that is comparable with that of an electric current through a solid (see infrared emission). In contrast to free electrons in a conductive solid however, electrons involved in a gas discharge will often leave their (conduction) band due to fierce collisions between atoms or between an atom and a previously freed electron. The electric charge of the nucleus of an atom initially equals the sum of the charges of its surrounding electrons. When one of these electrons escapes in the process of a collision, the net charge of the remaining atom will become positive and such a positively charged atom is called an ion. Since atoms in a gaseous environment are not bound into a grid as they are in solids, their ions can move more or less freely through space and contribute to the net displacement of charge albeit in opposite direction and charge as electrons. In a basic configuration, a gas discharge occurs between two electrodes that are located at the outer ends of a sealed glass tube and between which a DC-voltage is applied. The electrode carrying the positive voltage is called the
anode while the other one is called the cathode. The potential difference causes an electric field between the electrodes and this field issues a force that attracts electrons in the cathode towards the anode. In case of a sufficiently strong field it is indeed possible that electrons are pulled out from the cathode and when there is a vacuum within the tube, these
electrons will travel towards the anode at an ever-increasing speed. Their trip will end when they collide with the anode and recombine with one of its atoms, releasing their energy with the radiation of a photon. Such a collision would not provide the ultraviolet radiation that is required for a sun-lamp however. To create an effective sun-lamp, the tube has to be filled with a gas, causing collisions between the gas atoms and the electrons that emerged from the cathode. The exact behaviour of an individual collision is hardly predictable but the number of possible variations has proven to be limited. When there is little energy in a collision, the gas atom will temporarily be deformed and tipped out of balance without any resisting change of its properties. Such so-called elastic collisions will happen when a gas atom collides with an electron that was not yet able to gain enough speed in the electric field between the electrodes. In a collision with more energy (or higher speed) an electron within the atom may get exited and make a transition to a higher orbit within its atom. Most of the excited states of an electron are unstable and after a short while the electron will return to its initial state while emitting a photon with an electromagnetic radiation that is characteristic for the given type of transition (see infrared emission). Certain types of excited states however, happen to be meta-stable which means that the electrons are able to stay in their new and higher orbit for a relatively long period of time. When such an excited electron gets hit by another free electron it may move over to an even higher level of energy or it may even escape from its atom, leaving the atom as a positively charged ion. Ionisation may occur even in a single collision when the collision speed is sufficiently high. After the ionisation of an atom by a free electron there are now two free electrons that each can take speed in the electric field again and can get involved in new collisions. In a relatively small number of occurrences a free electron may also be captured by an ion were it then takes over the place of a formerly escaped electron, again under the release of a photon with a characteristic electromagnetic radiation. With sufficiently high numbers of involved electrons and atoms all types of collisions and transitions will occur more or less at the same time. The relative contribution of the different types of photons to the total amount of electromagnetic radiation is a statistical property that depends on the environmental conditions. A change in these conditions like a lower or higher gas pressure or temperature will alter the likeliness of a certain type of transition but the number of possible transitions will stay the same. This limitation and the fact that a certain transition produces radiation
with its own characteristic wavelength results in a spectral distribution that is characterised by more or less clear defined spectral lines in contrast to the more continuous spectral distribution of a glowing solid. For the construction of a sun-lamp it is essential that one or more of the stronger spectral lines are located within the ultraviolet area.
Mercury vapour meets this requirement with energy transitions whose corresponding wavelengths are located at 365 and 313 nanometers.
The electrical resistance of the filament of an incandescent lamp increases with temperature. This stabilises the current through the filament when a constant voltage is applied over it (see infrared emission). An electrical gas discharge often lacks this stabilising behaviour. The electrical resistance of a discharge may either increase or decrease with increasing currents, depending on the actual size of the current. When the resistance decreases at constant voltage, the current increases as a result and the temperature of the medium increases subsequently. Due to its negative temperature coefficient the resistance decreases even further, which again leads to an increase in current. This process continues until current and/or temperature reach the point where the tube or the electrodes will break down. To interrupt this devastating chain reaction the current has to be limited to a save level and the simplest way to achieve this is to connect a stabilising electric ballast in series with the discharge tube. The resistance of such a ballast must increase with rising currents or
temperatures or at least it must stay the same (see electrical circuits). In the figure next to here a simplified representation of the voltage-current characteristic of a gas discharge tube is given. For a better understanding the presentation of the various discharge transitions is drawn disproportional. Also the transitions at the breakdown points D and G of the characteristic are idealised and drawn sharper than would be the case in reality. The
diagonal straight lines represent the voltage-current characteristic of the serial resistor at different values of the supply voltage U. At I=0 the voltage over the resistor UR will be zero. At UL=0 UR will be equal to the supply voltage and, according to Ohm's law, the maximum current U/R will flow through the resistor. In a stable situation F, UR is equal to U minus UL and that is on the crossing point of both characteristics. When the supply voltage is zero there is no electric field and there will flow no current through the discharge tube. This corresponds with point A of the characteristic.
Despite the lack of an electric field however, a limited number of electrons will still be freed from their atoms due to the always-present gamma- and cosmic radiation. When a small supply voltage is now applied over the electrodes, a resulting weak electric field will cause these electrons to drift into the direction of the anode. In point B of the characteristic this current has reached its maximum. The number of free electrons now only depends on the natural background radiation and a further increase of the voltage causes no further effect
until point C of the characteristic. This type of current is called a dark- or Townsend discharge after the scientist John S. Townsend who profoundly studied this phenomenon.