A double Van de Graaff Generator

Introduction:

The electrostatic machine known as the Van de Graaff generator was invented by Robert J. Van de Graaff, in the USA, by 1929, with the objective of generating high voltages for experiments in nuclear physics. It was first described in a short abstract in the Physical Review, vol. 38, p. 1919, 1931, and in more detail in 1933 [p4]. The classical machine consists in a motorized insulating belt that transports charge to a hollow terminal. Inside the terminal the charge is collected by a row of points close to the belt and transferred to the exterior surface of the terminal by the Faraday "ice pail" effect. Charges are sprayed over the belt surface by another row of points below, connected to an electronic DC high-voltage supply. It is interesting to note that the original machine was double, with two terminals oppositely charged. More elaborated charging systems, as the use of current doublers and self-excited operation were also considered in [p4]. The machine was soon built in large scale as the Round Hill electrostatic generator [p3], that is now on display (mounted as an unipolar machine [p5]) at the Boston Museum of Science, in the USA.

The basic ideas of the machine can be traced to the 1800's or before, and particularly to Righi, who describes machines using rubber tubes with metallic rings [p55][p56] (1872) for charge transport with charge collectors inside hollow terminals, and also double tube machines and belt influence machines [p59] (1875). Another important antecessor is the Carré machine (1868), that uses a charge collector close to the terminal instead of inside it, a disk for charge transport, and a friction machine as high voltage supply, using influence to charge the disk from a grounded row of points. Friction belt machines were known since the 1700's, as in the machine made by Rouland by 1785 [50].

After the initial experiments with generators operating in air, high-power Van de Graaff generators were built, operating in tanks of compressed air, and later other gases, achieving several megavolts of output voltage and much higher output current than would be possible in the basic machine [p98]. An important improvement was the use of equipotential rings along the insulating support and even along the belt runs. The rings, biased at linearly varying voltages along the support by strings of resistors or corona points, emulate a supporting column with uniform resistivity and distribute evenly the potential developed at the terminal. Machines of this type continue to be used today, as power supplies for particle accelerators [p100], X-ray generators [p99], and similar applications.

The excitation system for the machine can be built in many ways. There is the original, and best, using an electronic excitator to spray charge in the belt, and many other possibilities, that can be identified with the charging systems of the classic friction and influence machines. This picture shows some of the possibilities. The friction system is very popular and simple, charging the lower roller by rolling friction with the belt.The charged roller then attracts opposite charge to the surface of the belt through a grounded comb or brush. The performance with this system is, however, quite impredictable. Other two methods, that I call the Holtz and Toepler methods, adapt the charging systems of their classic influence machines. Both rollers are conductive and insulated, and the machine can produce any polarity at the terminal. In the Holtz system, the charges in the belt polarize the rollers, and eventually leak to them, leaving then oppositely charged. In the Toepler system, charges at the surface of the belt are directly taken to charge them. The charged rollers then charge the belt surface with opposite charges at each end through brushes or combs.The systems that charge a roller with charges coming from the belt reaching it and use the charged roller as inductor to charge the belt going away from it are called "current doublers". Another system copies the charging mechanism of the Wimshurst machine (actually one half of the machine), or of the Holtz machine of the second kind. Each charged belt run attracts opposite charges to the surface of the other, with a reinforcing effect caused by electric field concentration at the combs or brushes. This method works well and is common in small laboratory machines.

The Van de Graaff generator is common in a variety of tabletop models for demonstrations and experiments with electrostatics, usually in unipolar configuration. Many descriptions of the most usual systems can be found in the web. I decided to built a machine that is not necessarily better, but is different from the usual designs seen today and closer to the original machine.

A double Van de Graaff machine:

In June 1999 I started to experiment with a double Van de Graaff machine. A double machine shall be able to produce greater potential differences than an unipolar machine for a given terminal size, because each terminal is charged to only one half of the total potential difference. My design uses two aluminum globes made by metal spinning, with 13.5 cm of diameter. This is enough for 202.5 kV at each terminal (30 kV/cm of radius), or more than 400 kV of potential difference.

The complete machine is composed of two identical, mirror-image units, that can be interconnected in several ways that cause the machines to charge with opposite polarities. In each unit, the terminal is mounted over a varnished PVC column, with the belt running outside it. This allows easier access to the belt, for observations, cleaning, and experiments, allows the use of a wider belt for more charging current, and minimizes the charge loss through the column, that has small diameter (1") and the interior sealed. The tube can be removed from the nylon plugs at its ends, what reduces the size of the machine for storage, and removes the tension from the belt. There is an evident problem of little insulation between the belt and the terminal, but I wanted to see what would happen. The belt enters the terminal through two slits with rounded borders. Each unit was initially assembled with identical current doublers below and above (Toepler system), and in the absence of major losses should be capable of sustained self-excited operation with any polarity at the terminal.

The upper and lower pulley assemblies, except for mounting details, are identical. The pulleys were made in nylon with 4 cm of diameter and 4.5 cm of length, and crowned by 1 degree angular cuts at the outer 1.5 cm of each side. The centers of the pulleys were covered by layers of adhesive aluminum foil, electrically connected to the axles by pins passing through radial holes at the centers of the pulleys. The pulleys were fixed by pressure over 1/4" steel axles. The axles were supported by ball bearings, fixed by pressure, that were glued in holes in the acrylic supports. The same supports hold two charge collectors each, one at each side of each pulley. One of the collectors, the charging or doubler comb, is connected to the adjacent axle, and the other, the spray comb, is connected in the lower assemblies to an insulated bar, and in the upper assemblies to the terminals. The charge collectors are made with serrated aluminum foil wrapped over 3/16" brass bars and held in place by plastic tubes that have a lengthwise cut. The lower pulleys are driven by belt and pulley systems by 12 V DC motors, that can move the belts at 3-5 turns per second. Electrical insulation is provided by the use of large nylon pulleys. Speed is controlled by varying the voltage applied to the motors. The belts have 4 cm of width, and were made with a kind of gray latex material used for physiotheraphic exercises (Thera band), joined with cyanoacrylate glue in 45 degrees joints with 5 mm overlaps. It appears that newer versions of this material, and several similar materials, have an anti-static coating, turning them useless for this purpose. In general, materials with something printed on them shall be avoided. Pure natural rubber, or latex, works well, and can be glued with "contact" glue. The best way to glue the joint is to first glue both ends to rigid plates (metal, plastic, etc.) with a weak glue at the sides opposite to the ones to be glued. The rigid plates help in the precise positioning of the flexible belt material during the gluing procedure and can be easily removed afterwards.

Pictures of the machine:

A single unit, and both units.
The bases: motor side, connections side.
The terminals: the slits, opening, internal assembly.
Excitation of a single unit by spray, and by induction, using a Toepler 2 disks machine.
Excitation of the double machine by charging one pulley (detail), and charging both pulleys.

Performance:

The units don't work reliably in self-excited influence mode, apparently because the upper current doublers don't work, with corona from the terminals at the slits canceling the charges that would travel in the down-going belts. But the units get easily charged to very high voltage if excited by a small electrostatic machine. The excitation of a single unit can be by spraying charge in the up-going belt with the lower pulley grounded, or by charging the lower pulley and grounding the charging comb. A single unit charged negatively can produce faint sparks to a grounded object with about 15-20 cm of length. The charging current was measured as 3-5 uA, what is consistent with the theoretical expected value. When a terminal is positive, corona plumes can be observed starting at the back of the up-going belt and spreading out for about 10 cm or more below the terminal, accompained by a cracking sound. A negative terminal is silent.

Both units can be excited to opposite polarities by charging the lower pulley of one unit, interconnecting the lower spray combs of both, and grounding the lower pulley of the other. It is also possible to charge both lower pulleys with opposite voltages, grounding both lower spray combs. There are other possibilities too. It is difficult to obtain long sparks between both terminals, despite the high voltage difference, unless a small ball (3-4 cm) is attached to the positive terminal. This results in sparks with up to 20 cm of length between the small ball and the other terminal. Long sparks are faint, with the appearance of a plume with the stem at the positive end, and only visible in the dark, because the terminals alone don't store much charge. High voltage Leyden jars attached to the terminals may improve this, but it is not simple to attach jars to the terminals without introducing significant losses at that very high voltage. A single unit can easily make all my current jars spark over. Long discharges between the normal terminals take the form of curious faint plumes that make a curve below the terminals, sometimes touching part of the up-going belts. These discharges, probably starting at the belts and entry slits, discharge the terminals preventing direct long sparks between them.

An impressive experiment with Leyden jars: With a positive terminal, long corona plumes appear below the terminal. A small Leyden jar held by its outer plate and with the terminal close to these plumes, maybe 10 cm away from the terminal or more, gets quickly charged to more voltage that it can sustain, and sparks over (terminal to border of outer foil) with a violent spark, while held in the hand. The operator doesn't receive any shock.

Improving the machine

In May 2002, I replaced two of the rollers by Teflon rollers, below in one unit and inside the terminal in the other. I also increased a bit the crowning of the pulleys with 2 degrees cuts, increased the tension in the belts, and used a better power supply for the motors. With this I obtained two units that work reliably using excitation by rolling friction. The Teflon rollers become negatively charged, and so the unit with the Teflon roller below generates positive charge at the terminal, and the other unit generates negative charge. I kept the current doublers, even with the Teflon rollers. The units generate similar voltages and charge with the same current. Both units operate interconnected through the lower spray combs, that can be grounded or floating with identical results.

The negative unit gets charged first and works a bit better, possibly due to smaller losses. It also works better with the comb in the lower current doubler disconnected. Apparently, the poor insulation of the nylon roller used in the doubler causes losses by currents that discharge the roller through the path roller - doubler comb - nylon surface of the roller - spray comb. With the comb disconnected the doubler works by the Holtz system, with smaller losses because a current discharging the roller metal surface would have to track under the belt to reach the exposed nylon surface and the spray comb. The current doubler on this unit evidently works, and most of the charging current comes from it. The machine practically stops if the lower pulley is grounded. The pulley must be well insulated, with the support and specially the insulating pulley driven by the motor clean and dry.

The positive unit (left) shows a curious phenomenon. It charges slowly at first, but after some time suddenly charges to the maximum voltage and keeps it. A possible cause is the operation of the current doubler mounted in the Teflon roller below, that starts to operate, even with an insulating roller, after the voltage gets high enough. The connection or not of the doubler comb inside the terminal doesn't have any observable effect.

The units produce faint sparks between the terminals with up to 20 cm with the help of a small ball attached to the positive terminal, and up to 9 cm sparks, more visible, directly (~180 kV of voltage difference). With greater spacings corona bursts are seen between the slits where the belts enter the terminals. This is the same behavior of the original machine.

Energy in a Van de Graaff generator:

Many people don't realize that these machines can produce dangerous shocks. The danger of an impulsive shock is proportional to the energy that it discharges, with about 10 Joules of energy being considered dangerous [10]. The energy stored at the terminal of a Van de Graaff generator can be calculated as E= 0.5CV², where C is the distributed capacitance of the terminal and V its voltage relative to ground. The capacitance of a sphere is given by C = 4pe₀r, where e₀ = 8.85x10^-12 and r is the radius of the sphere (meters), resulting in C = 111.2r pF. The maximum voltage that the machine can produce is limited by the electric field E at the surface of the terminal. For a sphere, voltage and electric field are associated by V = Er. Assuming the maximum electric field in air as E_max = 3 MV/m, V = 3x10⁶r. Combining these expressions, the stored energy is obtained as E = 500.4r³. E = 10 J would then correspond to r = 0.27 m. A machine with a terminal larger than this, and small losses, would be dangerous, with the danger increasing rapidly, with the cube of the radius.

With r = 6.75 cm, One terminal of my machine stores at most 0.1539 J. Enough for unconfortable shocks, but not dangerous.

Required mechanical power and charging current:

An estimation of the required mechanical power to move the charged belt, to be added to the power required to move the uncharged belt, is simply P = VI, where V is the terminal voltage and I is the belt current. Assuming the belt operating at the maximum charge density and transporting current upwards only, I = e₀E_maxWv, where W is the effectively used belt width and v is the belt speed. Considering that the maximum terminal voltage is V=E_maxr, P = e₀E_max²rWv.
For a driving pulley with diameter d, turned at a rotations per minute (rpm), v = (a/60)pd, resulting in P = e₀E_max²(p/60)rWda. The charging current is I = e₀E_max(p/60)Wda.
Note that the power is proportional to the cube of the "size" of the machine, the voltage is proportional to the size, and the current is proportional to the square of the size, if the proportions and the motor speed are retained. This happens with all electrostatic machines.
The length of the belt, or the height of the terminal, have no influence if the motor speed is constant (except for insulation, and a small effect on the output voltage, not considered). The length L appears in the formula for the current in the form I = e₀E_maxWLn, where n is the number of belt turns per second. The power is then P = e₀E_max²rWLn

For my machines, ignoring the doublers, with r = 0.0675 m, W = 0.034 m, L = 0.969 m, and n = 4, the predictions are I = 3.5 uA and P = 709 mW

The current agrees precisely with measurements. The power is difficult to evaluate, since the mechanical losses are large, the maximum voltage is not reached, and some power is spent to separate the belt from the charged rollers. In a single unit (the positive), the measured input power for the motor, with 6 V and 0.64 A, is 3.84 W. With the terminal uncharged and the lower spray comb disconnected (no charging current), the current decreases to 0.59 A and the power decreases to 3.54 W, indicating a difference of 300 mW. The terminal sparks to the grounded terminal of the other unit with 4 cm sparks, what corresponds to about 100 kV of voltage, corresponding to 350 mW of predicted input power. Close to the measured value, given the uncertainties of the measurements.

Comparison with other machines:

In comparison with other electrostatic machines operating in air, it's certain that for the production of very high voltages the Van de Graaff machine is the logical choice. But this is not so if all that is wanted is a convenient power supply for experiments with electrostatics or a machine that can produce long sparks. In comparison with most of the classical disk machines, a motorized VDG machine is noisy and mechanically problematic, the generated current is very small, the charge stored in the terminal is insufficient for long solid sparks, the output is unipolar, and the structure is inconvenient for connection to other devices. A disk machine as a triplex Wimshurst or a Bonetti machine with similar size can easily produce equivalent voltages (if sufficiently insulated), at both polarities, at much higher current.

Created: June 1999.
Last update: 27 March 2007
Antonio Carlos M. de Queiroz
http://www.coe.ufrj.br/~acmq

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