物理读数报告

What drives us to the future?

A Brief Look into Solar Energy & Fusion

2006011291| Qing Pei

Department of Computer Science & Technology, Tsinghua University, Beijing, PRC, 10084

Abstract: This paper mainly discusses about solar energy and fusion and their perspective as future sources of energy. With a look into both ways of energy conservation, a comparison on several aspects is given. The author’s attitude toward the future use of the two sources of energy is finally stated based on the foregoing discussion.

Keywords: energy, solar energy, fusion

Table of Contents

Prolegomenon. 3

What do We Need?. 3

Solar Energy: right around us. 5

An Inexhaustible Energy Source. 5

How do we collect solar energy?. 5

Fusion: a tiny sun. 7

The Real Sun versus The Artificial One. 11

Conclusion. 12

Bibliography. 12

Acknowledgement 12


Prolegomenon

The world is developing faster than ever. We need more and more energy to drives us to the future. Some scientists have already pointed out the problem facing us, energy shortage, as early as several decades ago. The exhaustion of the fossil fuels will soon come. We need a new energy source. It is expected to be green, stable and conservable. Some advances in this field have been there so far. Two of the optional energy sources, solar energy and fusion, I think, is important. Here I want to scan these two sources and compare them. The conclusions, I hope, either proved or disproved in the future, can help me understand the situation better.

What do We Need?

What do need to solve the problem? Simply, we need a new source of energy. The quality of the energy is still unclear in this answer. Some further look into the problem will help us see what we really desire.

How much energy do we need? This is a difficult question to answer. Figures in the past, however, can be based on to predict the future. Here is one.

Country

1975

1980

1990

2000

USA

15.0

20.0

40.0

80.0

USSR

7.5

15.0

35.0

70.0

Germany

3.0

5.0

10.0

20.0

France

2.5

4.0

8.0

15.0

Canada

3.0

5.0

10.0

20.0

Japan

2.5

3.5

7.0

15.0

UK

2.0

3.0

5.0

10.0

India

0.5

1.0

4.0

16.0

China

0.1

2.0

6.0

20.0

Other Countries

13.9

21.5

35.0

60.0

Total

50.0

80.0

160.0

326.0

Table 1 Global estimated energy consumption in trillion KWH**[1]**

Here is another.

Critical Global data

1995

2040

Population

5×109

10×109

Energy consumption

350EJ

900EJ

Average individual energy consumption

2200W

3000W

Table 2 Situation analysis 1995 and prognosis of 2040**[2]**

From both tables, we can see the energy consumption is unbelievably huge. Another alert is the consumption has more an exponential increase than a linear one. This is making the problem more urgent.

What kind of energy? We are using fossil fuels almost everywhere in the world. We depend on it so much that the day it is used out will be like a doomsday to us. It won’t be long before that day. In fact, some people have even told us the estimated date. They give us, though their estimations vary, the same signal, we must have an INEXAUSTIBLE source of energy to rely on. At least it should leave the work for finding its substitute for another hundreds or thousands of years. The rapid development of human civilization will be sustainable only in this way.

Another fatal defect of the fossil fuels is the exhaust gas. The carbon inside the fossil fuels turns out to be CO2 in the air. This can be tragic. We are giving out more CO2 than the biosphere can deal with. The future energy should, therefore, be GREEN.

Besides, the collection, conversion and transmission of the energy must be feasible and economical since we are to use the energy in a large scale. Efforts should be made to ensure both the rich and the poor can afford the new source of energy.

Conclusion: We need an inexhaustible green source of energy to meet the booming demand for energy, the application of which should be both feasible and economical.

Solar Energy: right around us

An Inexhaustible Energy Source

The earth receives solar energy in the form of electromagnetic radiation. The solar energy density is about 1.353kW/m2 on the outer surface of the earth’s atmosphere[3] and up to 1.0kW/m2 on the lithosphere[4]. That is to say, the total sum of solar energy we get, even if we can only utilize as little as 1% of it, seems “too” much for us.

How do we collect solar energy?

If we just need heat, put something cool out in the sunshine and it will collect the energy. However, hot things cannot be heated this way. Neither can the process go far enough till it reaches the state we need. The efficiency of such a thermodynamic process is pretty low. The Carnot efficiency is

In the collection above, Thigh (temperature of the source) is not much higher than Tlow (temperature of the sink).

This low efficiency results from the low energy density. We must concentrate the energy to one point, or to make Thigh there much higher, to get higher power, or higher efficiency, needed in application. A simple method is to use lens. A magnifier is enough to heat a paper to its burning point. This might make some readers recall the childhood times if they had done such a little “physics experiment”. To make a bigger concentrator, “a parabolic reflector gives high concentration.”[5]

Electricity is easy to transmit and distribute. Solar energy, as a result, is expected to be converted to electricity in many cases. This conversion can be done in different ways.

Suppose the efficiency of each step is η1, η2 …, the overall efficiency is

The final energy we have in the form of electricity is

Let the efficiency of the direct conversion be η0. The final energy we have is

We have to work to convert the energy from one form to another. Each process is not 100 percent efficient, either. Normally, the more process steps, the more energy is lost.

We can draw a conclusion:

Therefore, the direct conversion is the choice. (The technical problem is yet to be solved.)

Photovoltaic cells, or solar cells, are usually used to convert solar energy to electricity. P-N junction solar cells catch the photons from sunlight. The energy absorbed makes hole-electron pairs near the P-N junction. The internal electric field forces the holes and electrons to displace in a certain direction. Voltage is generated. With the load connected, electron current flows and the load works.

Loferski’s formulation describes the current-voltage relation of the P-N junction:

where Isc is the current density; Nph the number of incident photons of frequency ν; EG the energy gap.

The open circuit voltage is

where I0 is the equal and opposite current in either direction at equilibrium and

With the increase of EG, Voc increases while Isc decreases. A maximum value of is decided by EG. To get a cell with higher voltage, we link the cells.

The maximum efficiency of a solar cell is 0.25 theoretically. Organic semiconductors do not need to be made in single crystal form. The disadvantage is their relative lack of efficiency (about 1%).[6] The lifetime of a cadmium sulphide cell ranges from 2 to 60 years.[7]

Despite the actual lower efficiency we can reach now, solar cells are more and more used in calculators and in such areas as Tibet and Inner Mongolia where solar energy is rich but the power supply insufficient.

Fusion: a tiny sun

Long before we tried to use the energy of fusion reaction, the stars had been using it. Fusion is now chosen as a future source of energy. It should be since it was the natural one.

The universe consists of more than 99% plasma[8] though it is only 3 Kelvin on average. Have a look at the starry sky, all the twinkling stars are giving out light because of fusion reaction.

On Nov 1, 1952[9], the first hydrogen bomb exploded. Human beings began the use the energy of fusion reaction.

The fusion of the hydrogen isotopes deuterium (D) and tritium (T) according to the reaction

produces 17.6MeV of energy.[10]

Other fusion reactions include

The fusion reaction rate per unit volume can be written

where n1 and n2 are the densities of species 1 and 2, respectively, and

is the fusion reactivity. Here v is the velocity, f is the velocity distribution function, and σ_f_ is the fusion cross section. It is usually adequate to use a Maxwellian distribution,

to evaluate ⧼σ_v_⧽, in which case the value of the integral depends only upon the temperature _T _of the plasma.[11]

The energy released in most fusion reaction, e.g. an H-bomb explosion, is too much to control. For peaceful use, the reaction must be under control. We have to make the energy flow stable. One method is the magnetic confinement.

In magnetic confinement, the ions move in a toroidal path in the outer magnetic field. The Lorentz force propels them to orbit in a round path. The electric field force makes it move in the normal direction of the surface which includes the round path.

DSC01296.pngThe movement can be described by the following equations:

Text Box: Figure 2 Closed toroidal confinement

where FE is the electric field force, FL the Lorentz force, q the charge of the ion, m the mass of the ion, B the magnetic field intensity. Its path is shown in Figure 2[12].DSC01333.png

Figure 3 Schematic design of stellerator plasma and magnetic coils**[13]**

DSC01334.png

Figure 4 Plasma in the ASDEX Upgrade tokamak**[14]**

Another method is the inertial confinement. The principle is simple: let the reactants react before the explosion. The realization is, however, difficult.

Unlike fission, fusion reaction has no critical mass. This makes small scale use of the energy of fusion reaction possible. Another problem comes: the Lawson Criterion for the commencement of fusion:

where n is the density of the fuel (n particles per unit volume), and τ is the minimum time during which they are confined together.[15]

Confinement Method

Magnetic Confinement

Inertial Confinement

n(cm-3)

1014~1016

1024~1026

Τ(sec)

0.01~1

10-10~10-12

Figure 5 Comparison between the two confinement method concerning n & T**[16]**

Either the relatively long T in magnetic confinement or the vast n in inertial confinement is reached the commencement condition at the moment.

There is still another obstacle in making a fusion power plant. The plasma must be heated to a certain temperature, (or compressed to a certain density), to start the fusion reaction. Scientists have made laser guns and ion guns to provide the energy. Among them, NOVA in the US and AURORA in Russia can produce over 100kJ less than 1ns, fascinating but not enough for application. The dispersion and relatively low efficiency both make the task hard. The cost is too much as well.

The Real Sun versus The Artificial One

Source

Solar energy

Fusion

Availability

☆☆☆☆☆

☆☆☆☆☆

Power plant lifetime

☆☆☆☆

☆☆☆☆☆

On-the-go power supply

☆☆☆☆

(Tiny solar cells)

☆☆☆

(Stored in other media)

Safety Index

☆☆☆☆☆

☆☆☆☆

Pollutants after use

Zero

Zero

Maximum Power

☆☆☆

(Need concentration)

☆☆☆☆☆

(As the H-bomb shown…)

Cost

☆☆☆

(Lots of panels needed)

☆☆☆☆

(Complex design & a control system)

Feasibility

☆☆☆☆

(Already in use)

☆☆☆

(In labs but progresses made)

Figure 6 Comparison of solar energy and fusion

**Both **sources of energy seem, at least now, inexhaustible. The power plants both can last decades. With solar cells, we can gain solar energy on the go; confined fusion reaction needs a complex system, which seems impossible under the current technical condition. Solar energy is quite safe. The output of fusion reaction, in contrast, needs to be controlled to a relatively lower state than it is in the explosion of a hydrogen bomb. Otherwise it will probably cause danger. Neither the use of solar energy nor that of fusion produces pollutants as CO2, NOx or other exhaust gas. The resultant is just electron flow or helium. Fusion, without the restriction of critical mass, is better than fission in a power plant. It produces more energy per unit mass of reactant. The cost of building a power plant is a problem. A solar power plant takes up a large space since lots of solar panels are in it.

Both choices, however, need further improvement before practical use.

Conclusion

Solar energy and fusion both have a bright perspective. The two inexhaustible sources of energy will, once working, relieve the energy crisis. Research in this field is still advancing.

I tend to choose fusion as the main source of energy, as the alternative for heat-engine & hydroelectric plants, for it has an ample power output. Solar energy can work as a supplement in rural areas and for mobility use.

Bibliography

Agarwal, M. (1983). Solar Energy. New Dehli: S. Chand & Company Ltd.

Arons, J. d. (2007, March 15). The Metabolic Society. Beijing, China.

Bockris, J. O. (1980). Energy Options. New York: Halsted Press.

Ganchang, W. (2000). The Small Artifitial Sun, Inertial Confinement Fusion. Beijing, Tianhe: Tsinghua University Press, Jinan University Press.

McVeigh, J. (1984). Sun Power: An Introduction to the Applicaions of Solar Energy. (X. Wang, & X. Li, Trans.) National Defense Industry Press.

Weston M. Stacey, J. Fusion: an introduction to the physics and technology of magnetic confinement fusion.

Wilhelmsson, H. (2000). Fusion: A Voyage Through the Plasma Universe. London: Institute of Physics Publishing.

Acknowledgement

Special thanks to Qian Wenwen for suggestions in the composition of some sections and proof of the whole paper.


[1] (Agarwal, 1983, p. 3)

[2] (Arons, 2007, p. 13)

[3] (McVeigh, 1984, p. 15)

[4] (McVeigh, 1984, p. 19)

[5] (Agarwal, 1983, p. 33)

[6] (Bockris, 1980, p. 163)

[7] Table 8.IX (Bockris, 1980, p. 163)

[8] (Wilhelmsson, 2000, p. XV)

[9] (Ganchang, 2000, p. 60)

[10] (Weston M. Stacey)

[11] (Weston M. Stacey, p. 2)

[12] (Weston M. Stacey, p. 5)

[13] Plate 13 (Wilhelmsson, 2000)

[14] Plate 14 (Wilhelmsson, 2000)

[15] (Bockris, 1980, p. 100)

[16] Edited with reference to (Ganchang, 2000, p. 66)