Category Archives: Princeton

Kennedy’s perfect, boring college-entry essays

To get into any college you have to write an essay or two, generally including one describing why you want to go that particular college, and many students have trouble. How do I make myself stand out, they ask. My suggestion: Don’t. Make it clear that you want to go, but dare to be dull with the details. John Kennedy did; you can too.

JFK's dull letter to Harvard. It's his only essay.

JFK’s dull letter to Harvard. It’s his only essay.

Most school essays limit the number of words. The reviewer too prefers you keep it short. If you want to go to Harvard, or Princeton, or Iowa state, show you can say what needs to be said within the word limit. The first sentence must tell them that you want to go that college, specifically. Mention the college: you want to go to Old Ivy, say. Once that’s taken care of, just state your reasons. Unless you’re going into the writing program, the baldest, simplest terms will work just fine — e.g. that Old Ivy provides an excellent education. It’s better if you can mention a more-specific field of study, e.g. liberal arts or zoölogy, but that’s not necessary. You can now list three or so details to back up your claims. For example, you might mention that the zoölogy program at Old Ivy is well-regarded (mention the school often), that you enjoy their sports team (the ground-hogs, say), or their extracurriculars. Mention that your dad went there or your uncle (and is your hero — hero is a good word) or that you like the location. Surely there is some reason you want to go. If you can mention a famous teacher or alumnus, all the better. Flesh it out if you have space; don’t if you don’t. Conclude with a sentence pointing to the future: that this school will help me do something you want to achieve. You can be specific or not, but don’t lie. Dull is more effective than a lie. I’ve copied, above, John Kennedy’s essay to Harvard, and below his essay to Princeton. These essays follow the pattern, and are dull within the pattern. His conclusion for the first essay: that he wants to go to Harvard to be “a Harvard Man.” He got in. He used the same, dull letter for Princeton, but had more space. For Princeton he said It would have a good effect on me, and that he wanted to be “a Princeton Man.” He got into Princeton too, and went there for two months before switching to Harvard.

John F. Kennedy's, almost identical letter to Princeton. He got in there too.

John F. Kennedy’s, almost identical letter to Princeton. He got in there too.

You may think that letters like this only work if you are John F. Kennedy, and to some extent that is true. But not totally. I got into Princeton grad school from a background in public school, with no famous relatives or money. My grades were better than JFKs, but my essay had the same structure with some more specifics. As I recall, I explained that I wanted to go to Princeton because I wanted to study chemical engineering in a top department. I may have mentioned a famous professor, and stated I wanted to work on nuclear fusion — a big Princeton specialty at the time. That’s about all, as I recall.

This formula can be tweaked for the other college (and non-college) essays. I’ve previously written about the two speeches at the opening of the Gettysburg cemetery, in 1863. Edwin Everett gave the first speech of the day, excerpted and analyzed here. His speech followed the formula and was lauded. He told folks that it was important that we are here honoring the dead, and followed with three or four reasons for why it was important. His conclusion pointed to the future significance of the events. Republicans and Democrat listeners agreed this was a speech to remember from a scholar of note. Everett’s face graced the $50 bill for the 40 years after his death.

Abraham Lincoln also spoke at the Gettysburg dedication, but he didn’t follow the formula. He spoke of liberty, and America, and of a government of the people. His speech was panned at the time, even by Republicans. More details here. Though people now see his Gettysburg address as a landmark, at the time even the Republican press didn’t like it  Fortunately for Lincoln and the republic, they warmed to the speech over the next year – in time for the election of 1864. When you apply to college, you want entry now. You can’t wait a year for people to warm to your essay. Stick to the formula. You don’t want the compliment of finding, years from now, that one of the reviewers who rejected you remembers your words fondly. That will be too late. Write for the dull audience in front of you; help them put your application in the “accepted” box. As a last note: If you can not find any truthful reason that you want to go to Harvard or Old Ivy you probably should not be going there. The beginning of wisdom is self-knowledge, and the primary audience for your essay is you.

If you find you have good reasons, but find you need help with the process or with your english grammar, I should mention that my niece owns a company to help folks get into college — link here. She also has a book “From Public School to The Ivy League.

Robert E. Buxbaum, August 7, 2017. Some two years ago, I wrote an essay for my daughter on the joys and pressures of entering her junior year in high school. Here it is. 

Cornwallis attacks. Washington goes to Princeton.

In the previous post, I asked what you would do as a general (Cornwallis), December 27, 1776. You command 30,000 troops, some 12,000 at Princeton of at total 50,000 against Washington’s 3500. Washington is camped 12 miles to the south just outside of Trenton with a majority of his men scheduled to leave in three days when their enlistments expire.

In fact, what Cornwallis did, is what every commenter recommended. He attacked at Trenton, and lost New Jersey. Cornwallis left 2-3000 troops at Princeton and marched south. Despite fallen trees, swollen rivers, destroyed bridges — all courtesy of Washington’s men –Cornwallis reached Trenton and attacked. By the time he got there, 2000 of Washington’s men had left, partially replaced by untrained militia. After a skirmish, Washington set up 400 militia to keep the fires burning, and without telling them where he was going “Fall back if the British attack”, he took the rest of his forces east, across frozen fields and swampland, then north to Princeton along the Quaker-bridge road. He later said the reason was to avoid looking like a retreat.

He split his forces just outside of Princeton, and a detachment, led by Hugh Mercer and 350  regulars had the first battle as they ran into the 17th and 55th British regiments as they prepared to escort supplies to Trenton. The British commander, Lt.colonel Mawhood, seeing how few men he faced, sent the 55th and most of the supplies back to Princeton, and led his men to shoot at the Americans from behind a fence. Mercer’s men fired back with rifles and cannon, doing little. Then, the trained British did what their training demanded: they rose up and charged the rebels with fixed bayonets. Mercer, having no bayonets, called “Retreat!” before being stabbed repeatedly, see painting. Mawhood’s men seized the cannon, turned it on the fleeing remnants of Mercer’s men.

General Mercer defeated at Princeton, as Washington shows up.

General Mercer defeated at Princeton, as Washington shows up.

It looked like a British victory, but then General Nathaniel Greene (the fighting Quaker) showed up with several hundred Pennsylvania militiamen. The militiamen had never seen battle, and many fled, after shooting into the British lines with rifles and another cannon and grape-shot. At this point it looked like a draw, but then, Washington himself joined the battle with two brigades of regulars: Hitchcock’s 253 New Englanders and Hand’s 200 Pennsylvania riflemen.

Washington managed to rally the fleeing Pennsylvanians; “Parade with us, my brave fellows! There is but a handful of the enemy and we will have them directly!” And Mawhood, now without most of his officers, ordered a last bayonet charge and fled down the Post Road to Trenton. Washington rode after for a bit “It’s a fine fox chase, my boys!”

James Peale, 1783. John Sullivan and his forces at Frog Hollow. Battle of Princeton

James Peale, 1783. John Sullivan and his forces at Frog Hollow. Battle of Princeton

The rest of the British along with Mawhood, met the rest of Washington’s men, lead by John Sullivan, at a place called Frog Hollow, near where Princeton Inn College (Forbes College) now stands. The Americans opened with grape-shot and the British put up little resistance. Those who did not surrender were chased into town, taking refuge in Nassau Hall, the central building of the university. Alexander Hamilton’s men (he’d been rejected by Princeton) took special enjoyment in shooting cannon into the building. A hole remains in the college walls and a cannonball supposedly decapitated a portrait of George II. About then the New Jersey militia broke in a door, and the British surrendered.

Washington had captured, killed, or destroyed most of three English regiments, took a wagon train of supplies, and left going north following a bit of looting. “Loyalists” were relieved of coins, liquor, shoes, blankets. They ate the breakfast prepared for the 40th, and were gone by 11 AM, heading north — to where?. Cornwallis returned before noon “in a most infernal sweat — running, puffing, blowing, and swearing.” His men looted the town again, but now what?

Was Washington headed to New Brunswick where a handful of British soldiers guarded Cornwallis’s supplies and a war chest of £70,000? He didn’t go directly, but perhaps by a circuitous route. Cornwallis went straight to New Brunswick and jealously guarded the place, its money and supplies. Washington meanwhile ran to safety in the Watchung Mountains outside Morristown. Cornwallis’s 17th claimed victory, having defeated a larger group, but Cornwallis gave up Princeton, Trenton, and the lives of the New Jersey loyalists. Rebels flocked to Washington. Loyalists were looted and chased. Hessians were shot in “a sort of continual hunting party.” Philip Freneau expressed the change thus:

When first Britannia sent her hostile crew; To these far shores, to ravage and subdue, 

We thought them gods, and almost seemed to say; No ball could pierce them, and no dagger slay.

Heavens! what a blunder—half our fears were vain; These hostile gods at length have quit the plain.

 

Robert Buxbaum. December 21, 2016. So now that you know what happened, what SHOULD Cornwallis have done? Clearly, it’s possible to do everything right militarily, and still lose. This is an essence of comedy. The British had a similar Pyrrhic victory at Bunker Hill. I suspect Cornwallis should have fortified Trenton with a smaller force; built a stockade wall, and distributed weapons to the loyalists there. That’s a change in British attitude, but it’s this dynamic of trust that works. The British retreat music, “the world turned upside down“, is a Christmas song.

From Princeton: dare to be dumb.

Let’s say you have a good education and a good idea you want to present to equally educated colleagues. You might think to use your finest language skills: your big words, your long sentences, and your dialectically organized, long paragraphs. A recent, Princeton University study suggests this is a route to disaster with the educated, and even more so with the un-educated. In both groups, big words don’t convince, and don’t even impress, like small words do.

Most people won't care what you know unless they know that you care.

Like this fellow, most folks aren’t impressed by fancy speeches. (cartoon by Gahan Wilson)

http://web.princeton.edu/…/Opp%20Consequences%20of%20Erudit…

People, even educated ones, want ideas presented in simple words and simple sentences. They trust such statements, and respect those who speak this way more than those who shoot high, and sometimes over their heads. Even educated people find long words and sentences confusing, and off-putting. To them, as to the less-educated, it sounds like you’re using your fancy english as a cover for lies and ignorance, while trying to claim superiority. Who knew that George W. was so smart (Al Gore?). Here’s George W. at the SMU graduation yesterday (May 18). He does well, I’d say, with mostly one-syllable words.

This is the sort of advertising that people notice -- and trust.

Lower yourself to be one of the crowd, but don’t go so far that you’re the butt of jokes.

Reading this study, I’ve come to ask why fancy language skills is so important for getting into  college, and why it adds points when writing a college paper. Asked another way, why are professors pleased by something that’s off-putting to everyone else. One thought: this is a club initiation — a jargon to show you belong to the club, or want to. Alternately, perhaps professors have gotten so used to this that it’s become their natural language. Whatever the reason, when outside of university, keep it simple (and) stupid.

Some specifics: at job interviews, claim you want to work at their company doing a job in your field. Only when dealing with professors can you claim your goal is capitalizing on your intellectual synergies, and phrase that means the same thing. Don’t say, you’ll do anything, and remember it’s OK to ask for training; poor education doesn’t hold-back American productivity.

Dr. Robert E. Buxbaum, May 19, 2015. Here are some further thoughts on education, and some pictures of my dorm and the grad college at Princeton back in the day.

Entropy, the most important pattern in life

One evening at the Princeton grad college a younger fellow (an 18-year-old genius) asked the most simple, elegant question I had ever heard, one I’ve borrowed and used ever since: “tell me”, he asked, “something that’s important and true.” My answer that evening was that the entropy of the universe is always increasing. It’s a fundamentally important pattern in life; one I didn’t discover, but discovered to have a lot of applications and meaning. Let me explain why it’s true here, and then why I find it’s meaningful.

Famous entropy cartoon, Harris

Famous entropy cartoon, Harris

The entropy of the universe is not something you can measure directly, but rather indirectly, from the availability of work in any corner of it. It’s related to randomness and the arrow of time. First off, here’s how you can tell if time is moving forward: put an ice-cube into hot water, if the cube dissolves and the water becomes cooler, time is moving forward — or, at least it’s moving in the same direction as you are. If you can reach into a cup of warm water and pull out an ice-cube while making the water hot, time is moving backwards. — or rather, you are living backwards. Within any closed system, one where you don’t add things or energy (sunlight say), you can tell that time is moving forward because the forward progress of time always leads to the lack of availability of work. In the case above, you could have generated some electricity from the ice-cube and the hot water, but not from the glass of warm water.

You can not extract work from a heat source alone; to extract work some heat must be deposited in a cold sink. At best the entropy of the universe remains unchanged. More typically, it increases.

You can not extract work from a heat source alone; to extract work some heat must be deposited in a cold sink. At best the entropy of the universe remains unchanged.

This observation is about as fundamental as any to understanding the world; it is the basis of entropy and the second law of thermodynamics: you can never extract useful work from a uniform temperature body of water, say, just by making that water cooler. To get useful work, you always need something some other transfer into or out of the system; you always need to make something else hotter, colder, or provide some chemical or altitude changes that can not be reversed without adding more energy back. Thus, so long as time moves forward everything runs down in terms of work availability.

There is also a first law; it states that energy is conserved. That is, if you want to heat some substance, that change requires that you put in a set amount of work plus heat. Similarly, if you want to cool something, a set amount of heat + work must be taken out. In equation form, we say that, for any change, q +w is constant, where q is heat, and w is work. It’s the sum that’s constant, not the individual values so long as you count every 4.174 Joules of work as if it were 1 calorie of heat. If you input more heat, you have to add less work, and visa versa, but there is always the same sum. When adding heat or work, we say that q or w is positive; when extracting heat or work, we say that q or w are negative quantities. Still, each 4.174 joules counts as if it were 1 calorie.

Now, since for every path between two states, q +w is the same, we say that q + w represents a path-independent quantity for the system, one we call internal energy, U where ∆U = q + w. This is a mathematical form of the first law of thermodynamics: you can’t take q + w out of nothing, or add it to something without making a change in the properties of the thing. The only way to leave things the same is if q + w = 0. We notice also that for any pure thing or mixture, the sum q +w for the change is proportional to the mass of the stuff; we can thus say that internal energy is an intensive quality. q + w = n ∆u where n is the grams of material, and ∆u is the change in internal energy per gram.

We are now ready to put the first and second laws together. We find we can extract work from a system if we take heat from a hot body of water and deliver some of it to something at a lower temperature (the ice-cube say). This can be done with a thermopile, or with a steam engine (Rankine cycle, above), or a stirling engine. That an engine can only extract work when there is a difference of temperatures is similar to the operation of a water wheel. Sadie Carnot noted that a water wheel is able to extract work only when there is a flow of water from a high level to low; similarly in a heat engine, you only get work by taking in heat energy from a hot heat-source and exhausting some of it to a colder heat-sink. The remainder leaves as work. That is, q1 -q2 = w, and energy is conserved. The second law isn’t violated so long as there is no way you could run the engine without the cold sink. Accepting this as reasonable, we can now derive some very interesting, non-obvious truths.

We begin with the famous Carnot cycle. The Carnot cycle is an idealized heat engine with the interesting feature that it can be made to operate reversibly. That is, you can make it run forwards, taking a certain amount of work from a hot source, producing a certain amount of work and delivering a certain amount of heat to the cold sink; and you can run the same process backwards, as a refrigerator, taking in the same about of work and the same amount of heat from the cold sink and delivering the same amount to the hot source. Carnot showed by the following proof that all other reversible engines would have the same efficiency as his cycle and no engine, reversible or not, could be more efficient. The proof: if an engine could be designed that will extract a greater percentage of the heat as work when operating between a given hot source and cold sink it could be used to drive his Carnot cycle backwards. If the pair of engines were now combined so that the less efficient engine removed exactly as much heat from the sink as the more efficient engine deposited, the excess work produced by the more efficient engine would leave with no effect besides cooling the source. This combination would be in violation of the second law, something that we’d said was impossible.

Now let us try to understand the relationship that drives useful energy production. The ratio of heat in to heat out has got to be a function of the in and out temperatures alone. That is, q1/q2 = f(T1, T2). Similarly, q2/q1 = f(T2,T1) Now lets consider what happens when two Carnot cycles are placed in series between T1 and T2, with the middle temperature at Tm. For the first engine, q1/qm = f(T1, Tm), and similarly for the second engine qm/q2 = f(Tm, T2). Combining these we see that q1/q2 = (q1/qm)x(qm/q2) and therefore f(T1, T2) must always equal f(T1, Tm)x f(Tm/T2) =f(T1,Tm)/f(T2, Tm). In this relationship we see that the second term Tm is irrelevant; it is true for any Tm. We thus say that q1/q2 = T1/T2, and this is the limit of what you get at maximum (reversible) efficiency. You can now rearrange this to read q1/T1 = q2/T2 or to say that work, W = q1 – q2 = q2 (T1 – T2)/T2.

A strange result from this is that, since every process can be modeled as either a sum of Carnot engines, or of engines that are less-efficient, and since the Carnot engine will produce this same amount of reversible work when filled with any substance or combination of substances, we can say that this outcome: q1/T1 = q2/T2 is independent of path, and independent of substance so long as the process is reversible. We can thus say that for all substances there is a property of state, S such that the change in this property is ∆S = ∑q/T for all the heat in or out. In a more general sense, we can say, ∆S = ∫dq/T, where this state property, S is called the entropy. Since as before, the amount of heat needed is proportional to mass, we can say that S is an intensive property; S= n s where n is the mass of stuff, and s is the entropy change per mass. 

Another strange result comes from the efficiency equation. Since, for any engine or process that is less efficient than the reversible one, we get less work out for the same amount of q1, we must have more heat rejected than q2. Thus, for an irreversible engine or process, q1-q2 < q2(T1-T2)/T2, and q2/T2 is greater than -q1/T1. As a result, the total change in entropy, S = q1/T1 + q2/T2 >0: the entropy of the universe always goes up or stays constant. It never goes down. Another final observation is that there must be a zero temperature that nothing can go below or both q1 and q2 could be positive and energy would not be conserved. Our observations of time and energy conservation leaves us to expect to find that there must be a minimum temperature, T = 0 that nothing can be colder than. We find this temperature at -273.15 °C. It is called absolute zero; nothing has ever been cooled to be colder than this, and now we see that, so long as time moves forward and energy is conserved, nothing will ever will be found colder.

Typically we either say that S is zero at absolute zero, or at room temperature.

We’re nearly there. We can define the entropy of the universe as the sum of the entropies of everything in it. From the above treatment of work cycles, we see that this total of entropy always goes up, never down. A fundamental fact of nature, and (in my world view) a fundamental view into how God views us and the universe. First, that the entropy of the universe goes up only, and not down (in our time-forward framework) suggests there is a creator for our universe — a source of negative entropy at the start of all things, or a reverser of time (it’s the same thing in our framework). Another observation, God likes entropy a lot, and that means randomness. It’s his working principle, it seems.

But before you take me now for a total libertine and say that since science shows that everything runs down the only moral take-home is to teach: “Let us eat and drink,”… “for tomorrow we die!” (Isaiah 22:13), I should note that his randomness only applies to the universe as a whole. The individual parts (planets, laboratories, beakers of coffee) does not maximize entropy, but leads to a minimization of available work, and this is different. You can show that the maximization of S, the entropy of the universe, does not lead to the maximization of s, the entropy per gram of your particular closed space but rather to the minimization of a related quantity µ, the free energy, or usable work per gram of your stuff. You can show that, for any closed system at constant temperature, µ = h -Ts where s is entropy per gram as before, and h is called enthalpy. h is basically the potential energy of the molecules; it is lowest at low temperature and high order. For a closed system we find there is a balance between s, something that increases with increased randomness, and h, something that decreases with increased randomness. Put water and air in a bottle, and you find that the water is mostly on the bottom of the bottle, the air is mostly on the top, and the amount of mixing in each phase is not the maximum disorder, but rather the one you’d calculate will minimize µ.

As the protein folds its randomness and entropy decrease, but its enthalpy decreases too; the net effect is one precise fold that minimizes µ.

As a protein folds its randomness and entropy decrease, but its enthalpy decreases too; the net effect is one precise fold that minimizes µ.

This is the principle that God applies to everything, including us, I’d guess: a balance. Take protein folding; some patterns have big disorder, and high h; some have low disorder and very low h. The result is a temperature-dependent  balance. If I were to take a moral imperative from this balance, I’d say it matches better with the sayings of Solomon the wise: “there is nothing better for a person under the sun than to eat, drink and be merry. Then joy will accompany them in their toil all the days of the life God has given them under the sun.” (Ecclesiastes 8:15). There is toil here as well as pleasure; directed activity balanced against personal pleasures. This is the µ = h -Ts minimization where, perhaps, T is economic wealth. Thus, the richer a society, the less toil is ideal and the more freedom. Of necessity, poor societies are repressive. 

Dr. Robert E. Buxbaum, Mar 18, 2014. My previous thermodynamic post concerned the thermodynamics of hydrogen production. It’s not clear that all matter goes forward in time, by the way; antimatter may go backwards, so it’s possible that anti matter apples may fall up. On microscopic scale, time becomes flexible so it seems you can make a time machine. Religious leaders tend to be anti-science, I’ve noticed, perhaps because scientific miracles can be done by anyone, available even those who think “wrong,” or say the wrong words. And that’s that, all being heard, do what’s right and enjoy life too: as important a pattern in life as you’ll find, I think. The relationship between free-energy and societal organization is from my thesis advisor, Dr. Ernest F. Johnson.

Nuclear fusion

I got my PhD at Princeton University 33 years ago (1981) working on the engineering of nuclear fusion reactors, and I thought I’d use this blog to rethink through the issues. I find I’m still of the opinion that developing fusion is important as the it seems the best, long-range power option. Civilization will still need significant electric power 300 to 3000 years from now, it seems, when most other fuel sources are gone. Fusion is also one of the few options for long-range space exploration; needed if we ever decide to send colonies to Alpha Centauri or Saturn. I thought fusion would be ready by now, but it is not, and commercial use seems unlikely for the next ten years at least — an indication of the difficulties involved, and a certain lack of urgency.

Oil, gas, and uranium didn’t run out like we’d predicted in the mid 70s. Instead, population growth slowed, new supplies were found, and better methods were developed to recover and use them. Shale oil and fracking unlocked hydrocarbons we thought were unusable, and nuclear fission reactors got better –safer and more efficient. At the same time, the more we studied, the clearer it came that fusion’s technical problems are much harder to tame than uranium fission’s.

Uranium fission was/is frighteningly simple — far simpler than even the most basic fusion reactor. The first nuclear fission reactor (1940) involved nothing more than uranium pellets in a pile of carbon bricks stacked in a converted squash court at the University of Chicago. No outside effort was needed to get the large, unstable uranium atoms split to smaller, more stable ones. Water circulating through the pile removed the heat released, and control was maintained by people lifting and lowering cadmium control rods while standing on the pile.

A fusion reactor requires high temperature or energy to make anything happen. Fusion energy is produced by combining small, unstable heavy hydrogen atoms into helium, a bigger more stable one, see figure. To do this reaction you need to operate at the equivalent of about 500,000,000 degrees C, and containing it requires (typically) a magnetic bottle — something far more complex than a pile of graphic bricks. The reward was smaller too: “only” about 1/13th as much energy per event as fission. We knew the magnetic bottles were going to be tricky, e.g. there was no obvious heat transfer and control method, but fusion seemed important enough, and the problems seemed manageable enough that fusion power seemed worth pursuing — with just enough difficulties to make it a challenge.

Basic fusion reaction: deuterium + tritium react to give helium, a neutron and energy.

Basic fusion reaction: deuterium + tritium react to give helium, a neutron and energy.

The plan at Princeton, and most everywhere, was to use a TOKAMAK, a doughnut-shaped reactor like the one shown below, but roughly twice as big; TOKAMAK was a Russian acronym. The doughnut served as one side of an enormous transformer. Hydrogen fuel was ionized into a plasma (a neutral soup of protons and electrons) and heated to 300,000,000°C by a current in the TOKOMAK generated by varying the current in the other side of the transformer. Plasma containment was provided by enormous magnets on the top and bottom, and by ring-shaped magnets arranged around the torus.

As development went on, we found we kept needing bigger and bigger doughnuts and stronger and stronger magnets in an effort to balance heat loss with fusion heating. The number density of hydrogen atoms per volume, n, is proportional to the magnetic strength. This is important because the fusion heat rate per volume is proportional to n-squared, n2, while heat loss is proportional to n divided by the residence time, something we called tau, τ. The main heat loss was from the hot plasma going to the reactor surface. Because of the above, a heat balance ratio was seen to be important, heat in divided by heat out, and that was seen to be more-or-less proportional to nτ. As the target temperatures increased, we found we needed larger and larger nτ reactors to make a positive heat balance. And this translated to ever larger reactors and ever stronger magnetic fields, but even here there was a limit, 1 billion Kelvin, a thermodynamic temperature where the fusion reaction went backward and no energy was produced. The Princeton design was huge, with super strong, super magnets, and was operated at 300 million°C, near the top of the reaction curve. If the temperature went above or below this temperature, the fire would go out. There was no room for error, but relatively little energy output per volume — compared to fission.

Fusion reaction options and reaction rates.

Fusion reaction options and reaction rates.

The most likely reaction involved deuterium and tritium, referred to as D and T. This was the reaction of the two heavy isotopes of hydrogen shown in the figure above — the same reaction used in hydrogen bombs, a point we rarely made to the public. For each reaction D + T –> He + n, you get 17.6 million electron volts (17.6 MeV). This is 17.6 million times the energy you get for an electron moving over one Volt, but only 1/13 the energy of a fission reaction. By comparison, the energy of water-forming, H2 + 1/2 O2 –> H2O, is the equivalent of two electrons moving over 1.2 Volts, or 2.4 electron volts (eV), some 8 million times less than fusion.

The Princeton design involved reacting 40 gm/hr of heavy hydrogen to produce 8 mol/hr of helium and 4000 MW of heat. The heat was converted to electricity at 38% efficiency using a topping cycle, a modern (relatively untried) design. Of the 1500 MWh/hr of electricity that was supposed to be produced, all but about 400 MW was to be delivered to the power grid — if everything worked right. Sorry to say, the value of the electricity did not rise anywhere as fast as the cost of the reactor and turbines. Another problem: 1100 MW was more than could be easily absorbed by any electrical grid. The output was high and steady, and could not be easily adjusted to match fluctuating customer demand. By contrast a coal plant’s or fuel cell’s output could be easily adjusted (and a nuclear plant with a little more difficulty).

Because of the need for heat balance, it turned out that at least 9% of the hydrogen had to be burnt per pass through the reactor. The heat lost per mol by conduction to the wall was, to good approximation, the heat capacity of each mol of hydrogen ions, 82 J/°C mol, times the temperature of the ions, 300 million °C divided by the containment time, τ. The Princeton design was supposed to have a containment of about 4 seconds. As a result, the heat loss by conduction was 6.2 GW per mol. This must be matched by the molar heat of reaction that stayed in the plasma. This was 17.6 MeV times Faraday’s constant, 96,800 divided by 4 seconds (= 430 GW/mol reacted) divided by 5. Of the 430 GW/mol produced in fusion reactions only 1/5 remains in the plasma (= 86 GW/mol) the other 4/5 of the energy of reaction leaves with the neutron. To get the heat balance right, at least 9% of the hydrogen must react per pass through the reactor; there were also some heat losses from radiation, so the number is higher. Burn more or less percent of the hydrogen and you had problems. The only other solution was to increase τ > 4 seconds, but this meant ever bigger reactors.

There was also a material handling issue: to get enough fuel hydrogen into the center of the reactor, quite a lot of radioactive gas had to be handled — extracted from the plasma chamber. These were to be frozen into tiny spheres of near-solid hydrogen and injected into the reactor at ultra-sonic velocity. Any slower and the spheres would evaporate before reaching the center. As 40 grams per hour was 9% of the feed, it became clear that we had to be ready to produce and inject 1 pound/hour of tiny spheres. These “snowballs-in-hell” had to be small so they didn’t dampen the fire. The vacuum system had to be able to be big enough to handle the lb/hr or so of unburned hydrogen and ash, keeping the pressure near total vacuum. You then had to purify the hydrogen from the ash-helium and remake the little spheres that would be fed back to the reactor. There were no easy engineering problems here, but I found it enjoyable enough. With a colleague, I came up with a cute, efficient high vacuum pump and recycling system, and published it here.

Yet another engineering challenge concerned the difficulty of finding a material for the first-wall — the inner wall of the doughnut facing the plasma. Of the 4000 MW of heat energy produced, all the conduction and radiation heat, about 1000 MW is deposited in the first wall and has to be conducted away. Conducting this heat means that the wall must have an enormous coolant flow and must withstand an enormous amount of thermal stress. One possible approach was to use a liquid wall, but I’ve recently come up with a rather nicer solid wall solution (I think) and have filed a patent; more on that later, perhaps after/if the patent is accepted. Another engineering challenge was making T, tritium, for the D-T reaction. Tritium is not found in nature, but has to be made from the neutron created in the reaction and from lithium in a breeder blanket, Li + n –> He + T. I examined all possible options for extracting this tritium from the lithium at low concentrations as part of my PhD thesis, and eventually found a nice solution. The education I got in the process is used in my, REB Research hydrogen engineering business.

Man inside the fusion reactor doughnut at ITER. He'd better leave before the 8,000,000°C plasma turns on.

Man inside the fusion reactor doughnut at ITER. He’d better leave before the 8,000,000°C plasma turns on.

Because of its complexity, and all these engineering challenges, fusion power never reached the maturity of fission power; and then Three-mile Island happened and ruined the enthusiasm for all things nuclear. There were some claims that fusion would be safer than fission, but because of the complexity and improvements in fission, I am not convinced that fusion would ever be even as safe. And the long-term need keeps moving out: we keep finding more uranium, and we’ve developed breeder reactors and a thorium cycle: technologies that make it very unlikely we will run out of fission material any time soon.

The main, near term advantage I see for fusion over fission is that there are fewer radioactive products, see comparison.  A secondary advantage is neutrons. Fusion reactors make excess neutrons that can be used to make tritium, or other unusual elements. A need for one of these could favor the development of fusion power. And finally, there’s the long-term need: space exploration, or basic power when we run out of coal, uranium, and thorium. Fine advantages but unlikely to be important for a hundred years.

Robert E. Buxbaum, March 1, 2014. Here’s a post on land use, on the aesthetics of engineering design, and on the health risks of nuclear power. The sun’s nuclear fusion reactor is unstable too — one possible source of the chaotic behavior of the climate. Here’s a control joke.

Tiger Sculpture at REB Research

Here’s the latest REB Research sculpture: a saber-toothed tiger:

Saber-toothed Tiger sculpture at REB Research; the face follows you (sort of). Another sculpture, a bit of our 3 foot geodesic is shown in the foreground.

Saber-toothed Tiger sculpture at REB Research; the face follows you. A bit of our 3 foot geodesic dome is shown in the foreground.

It’s face follows you (somewhat); It was inspired by my recent visit to Princeton Univ — they had lots of tiger statues, but none that looked eerie enough as you walked by. Click here for: YouTube movie.

Normally, by the way, REB Research makes hydrogen generators and other hydrogen stuff. May 1, 2013

Here are the Princeton PhD group of 1980. I’m the hairy bearded fellow at right who’s looking the wrong way. My thesis advisor, Ernest Johnson is the suited fellow just left of center. Dave Ollis is in front of me, and Joe Calo is in front of him, etc. Visit my Facebook page to see how my friends tagged themselves. 35 years ago!
Princeton Chemical Engineering Grad-students, late 1970s. My thesis advisor is the tall fellow at center; I'm the bearded fellow at right looking the wrong way.

Princeton Chemical Engineering Grad-students, late 1970s. My thesis advisor is the tall fellow at center; I’m the bearded fellow at right looking the wrong way.

The dining room, and my room at the Princeton Grad College.

I took these pictures at reunions this year 2012; the first shot is the dining room at the Princeton Grad college. They favored robes for formal dinners when I started; the fellows in white are waiters– and we had stewards to help clean up our rooms. (Mine knew Einstein). The second photo shows the courtyard looking towards two of my dorm rooms. One year I was in the second floor room at left with the bay window. One year in the second floor room at upper right (barely visible).

GC dining 2 my dormroom

And here is the Grad Tower — Otherwise known as “Cleveland Tower” to honor Princeton alumnus, Grover Cleveland, and here’s the fireplace in the dining room. Reminds one of The School of Witchcraft and Wizardry, in that book by JK Rowling– Boar-scabs, I think. The motto: bonus entra, melior exi: good coming, better leaving.

Grad tower  GC dining fireplace

Here’s my PhD class; at first glance, you would not think we belong.

Robert Buxbaum, June, 2012