The Helmholtz Coil and the Maxwell Coil

To do magnetic resonance imaging, you need a static magnetic field that is uniform and a switchable magnetic field that has a uniform gradient. How do you produce such fields? In this post, I explain one of the simplest ways: using a Helmholtz coil and a Maxwell coil.

Both of these are created using circular coils. The magnetic field B_z produced by a circular coil can be calculated using the law of Biot and Savart (see Chapter 8 of Intermediate Physics for Medicine and Biology)

where μ₀ is the permeability of free space (the basic constant of magnetostatics), I is the coil current, N is the number of turns, R is the coil radius, and z is the distance along the axis from the coil center.

The Helmholtz Coil

The Helmholtz coil consists of two circular coils in parallel planes, having the same axis and the same current in the same direction, that are separated by a distance d. Our goal will be to find the value of d that gives the most uniform magnetic field. By superposition, the magnetic field is 

 

To create a uniform magnetic field, we will perform a Taylor expansion of the magnetic field about the origin (z = 0). We will need derivatives of the magnetic field. The first derivative is

(The reader will have to fill in the missing steps when calculating these derivatives.) At z = 0, this derivative will go to zero. In fact, because the magnetic field is even about the z axis, all odd derivatives will be zero, regardless of the value of d.

The second derivative is

At z = 0, the two terms in the brackets are the same. Our goal is to have this term be zero, implying that the second order term in the Taylor series vanishes. This will happen if

or, in other words, d = R. This famous result says that for a Helmholtz pair the coil separation should equal the coil radius.

A Helmholtz coil produces a remarkably uniform field near the origin. However, it is not uniform enough for use in most magnetic resonance imaging machines, which typically have a more complex set of coils to create an even more homogeneous field. If you need a larger region that is homogeneous, you could always just use a larger Helmholtz coil, but then you would need more current to achieve the desired magnetic field at the center. A Helmholtz pair isn’t bad if you want to use only two reasonably sized coils.

The Maxwell Coil

The Helmholtz coil produces a uniform magnetic field, whereas the Maxwell coil produces a uniform magnetic field gradient. It consists of two circular coils, in parallel planes having the same axis, that are separated by a distance d, but which have current in the opposite directions. Again, our goal will be to find the value of d that gives the most uniform magnetic field gradient. The magnetic field is

The only difference between this case and that for the Helmholtz coil is the change in sign of the second term in the bracket. If z = 0, the magnetic field is zero. Moreover, the magnetic field is an odd function of z, so all even derivatives also vanish. The first derivative is

This expression gives us the magnitude of the gradient at the origin, but it doesn’t help us create a more uniform gradient. The second derivative is

This derivative is zero at the origin, regardless of the value of d. So, we have to look at the third derivative.

At z = 0, this will vanish if

or, in other words, d = √3 R = 1.73 R. Thus, the two coils have a greater separation for a Maxwell coil than for a Helmholtz coil. The Maxwell coil would be useful for producing the slice selection gradient during MRI (for more about the need for gradient fields in MRI, see Chapter 18 of IPMB).

Conclusion

Below is a plot of the normalized magnetic field as a function of z for the Helmholtz coil (blue) and the Maxwell coil (yellow). As you can see, the region with a uniform field or gradient is small. It depends on what level of accuracy you need, but if you are more than half a radius from the origin you will see significant deviations from homogeneity.
 

Russ Hobbie and I never discuss the Helmholtz coil in Intermediate Physics for Medicine and Biology. We don’t mention the Maxwell coil by name, but Problem 33 of Chapter 18 analyzed a Maxwell pair even if we don’t call it that.

The Maxwell coil is great for producing the magnetic field gradient dB_z/dz needed for slice selection in MRI, but how do you produce the gradients dB_z/dx and dB_z/dy needed during MRI readout and phase encoding? That, my friends, is a story for another post.

Mr. Clough

A teacher affects eternity; he can never tell where his influence stops. 

Henry Adams

Stephen Clough, from the 1975
Homestead Jr.-Sr. High School Yearbook.

How does someone end up being coauthor on a textbook like Intermediate Physics for Medicine and Biology? It takes a lot of friends, teachers, and role models who help you along the way. I had many excellent teachers when I was young. One of the best was Stephen Clough.

I attended grades 7–10 at Homestead Junior-Senior High School. Usually a junior high and senior high are in separate buildings, but the suburb of Fort Wayne where I lived at the time was new and growing, and had the two combined. For two years (I think grades 9 and 10) I had English with Mr. Clough. He was one of the younger teachers and had longish hair and a mustache, and I thought he was little bit of a hippie. That’s OK, because in the mid 70s hippies were still groovy (although they would go out of fashion soon).

Before I had Mr. Clough, I didn’t read much. I was obsessed with baseball and would read an occasional sports biography, but not much else. I did well in school, but I don’t remember our classes being too challenging or having much homework. Life was about hanging around with friends, playing ping pong, riding bikes, listening to music, and watching television. But Mr. Clough had us reading modern fiction, like Animal Farm and Lord of the Flies. For me, this was an intellectual awakening. Before Mr. Clough I rarely read books; after Mr. Clough I read all the time (and still do).

Me (age 15) from the 1975
Homestead Jr.-Sr. High School Yearbook.

I remember how, on Fridays, Mr. Clough would bring his guitar to school and play for us and sing. I thought this was the coolest thing I’d ever seen. None of my other teachers related to us like that. He played a lot of Dylan. I’ll never forget the day he explained what the words meant in the song American Pie. 

Mr. Clough had a huge influence on my academic development. Reading books led to reading the scientific writing of Isaac Asimov, which led to majoring in physics in college, which led to a PhD, which ultimately led to becoming a coauthor of Intermediate Physics for Medicine and Biology. I owe him much.

As Henry Adams said, a teacher affects eternity. I hope everyone teaching a class using IPMB keeps that in mind. You can never tell where your influence stops. 

I last saw Mr. Clough at my 30^th high school reunion. My friend from high school, Dave Small, became an opera singer, and he sang several songs for us at the gathering. Guess who accompanied him on the guitar? Stephen Clough.

American Pie, by Don McLean.

https://www.youtube.com/watch?v=PRpiBpDy7MQ

J. Robert Oppenheimer, Biological Physicist

J. Robert Oppenheimer.

Did you watch Oppenheimer in the theater this summer? I did. The movie told how J. Robert Oppenheimer led the Manhattan Project that built the first atomic bomb during World War II. But the movie skipped Oppenheimer’s research in biological physics related to photosynthesis.

Russ Hobbie and I only make a passing mention of photosynthesis in Chapter 3 of Intermediate Physics for Medicine and Biology.

The creation of glucose or other sugars is the reverse of the respiration process and is called photosynthesis. The free energy required to run the reaction the other direction is supplied by light energy.

From Photon to Neuron,
by Philip Nelson.

To learn more about Oppie and photosynthesis, I turn to Philip Nelson’s wonderful textbook From Photon to Neuron: Light, Imaging, Vision. His discussion of photosynthesis begins

Photosynthetic organisms convert around 10¹⁴ kg of carbon from carbon dioxide into biomass each year. In addition to generating the food that we enjoy eating, photosynthetic organisms emit a waste product, free oxygen, that we enjoy breathing. They also stabilize Earth’s climate by removing atmospheric CO₂.

Nelson begins the story by introducing William Arnold, Oppenheimer’s future collaborator.

W. Arnold was an undergraduate student interested in a career in astronomy. In 1930, he was finding it difficult to schedule all the required courses he needed for graduation. His advisor proposed that, in place of Elementary Biology, he could substitute a course on Plant Physiology organized by [Robert] Emerson. Arnold enjoyed the class, though he still preferred astronomy. But unable to find a place to continue his studies in that field after graduation, he accepted an offer from Emerson to stay on as his assistant.

Emerson and Arnold went on to perform critical experiments on photosynthesis. Then Emerson performed another experiment with [Charlton] Lewis, in which they found that chlorophyll does not absorb light with a wavelength of 480 nm (blue), but an accessory pigment called phycocyanin does. Emerson and Lewis concluded that “the energy absorbed by phycocyanin must be available for photosynthesis.”

Here is where Oppenheimer comes into the story. I will let Nelson tell it.

Could phycocyanin absorb light energy and somehow transfer it to the chlorophyll system?...

Arnold eventually left Emerson’s lab to study elsewhere, but they stayed in contact. Emerson told him about the results with Lewis, and suggested that he think about the energy-transfer problem. Arnold had once audited a course on quantum physics, so he visited the professor for that course to pose the puzzle. The professor was J. R. Oppenheimer, and he did have an idea. Oppenheimer realized that a similar energy transfer process was known in nuclear physics; from this he created a complete theory of fluorescence resonance energy transfer. Oppenheimer and Arnold also made quantitative estimates indicating that phycocyanin and chlorophyll could play the roles of donor and acceptor, and that this mechanism could give the high transfer efficiency needed to explain the data.

So, what nuclear energy transfer process was Oppenheimer talking about? In Arnold and Oppenheimer’s paper, they wrote

It is the purpose of the present paper to point out a mechanism of energy transfer from phycocyanin to chlorophyll, the efficiency of which seems to be high enough to account for the results of Emerson and Lewis. This new process is, except for the scale, identical with the process of internal conversion that we have in the study of radioactivity.

Internal conversion is a topic Russ and I address in IPMB. We said

Whenever a nucleus loses energy by γ decay, there is a competing process called internal conversion. The energy to be lost in the transition, E_γ, is transferred directly to a bound electron, which is then ejected.

Introductory Nuclear Physics,
by Kenneth Krane.

More detail can be found in Introductory Nuclear Physics by Kenneth Krane.

Internal conversion is an electromagnetic process that competes with γ emission. In this case the electromagnetic multipole fields of the nucleus do not result in the emission of a photon; instead, the fields interact with the atomic electrons and cause one of the electrons to be emitted from the atom. In contrast to β decay, the electron is not created in the decay process but rather is a previously existing electron in an atomic orbit. For this reason internal conversion decay rates can be altered slightly by changing the chemical environment of the atom, thus changing somewhat the atomic orbits. Keep in mind, however, that this is not a two-step process in which a photon is first emitted by the nucleus and then knocks loose an orbiting electron by a process analogous to the photoelectric effect; such a process would have a negligibly small probability to occur.

Nelson compares the photosynthesis process to another process widely used in biological imaging: Fluorescence resonance energy transfer (FRET). He describes FRET this way.

We can find pairs of molecular species, called donor/acceptor pairs, with the property that physical proximity abolishes fluorescence from the donor. When such a pair are close, the acceptor nearly always pulls the excitation energy off the donor, before the donor has a chance to fluoresce. The acceptor may either emit a photon, or lose its excitation without fluorescence (“nonradiative” energy loss).

Let’s put this all together. The donor in FRET is like the phycocyanin molecule in photosynthesis is like the nucleus in internal conversion. The acceptor in FRET is like the chlorophyll molecule in photosynthesis is like the electron cloud in internal conversion. The fluorescence of the donor/phycocyanin/nucleus is suppressed (in the nuclear case, fluorescence would be gamma decay). Instead, the electromagnetic field of the donor/phycocyanin/nucleus interacts with, and transfers energy to, the acceptor/chlorophyll/electron cloud. In the case of FRET, the acceptor then fluoresces (which is what is detected when doing FRET imaging). The chlorophyll/electron cloud does not fluoresce, but instead ejects an electron in the case of internal conversion, or energizes an electron that can ultimately perform chemical reactions in the case of photosynthesis. All three processes are exquisitely sensitive to physical proximity. For FRET imaging, this sensitivity allows one to say if two molecules are close to each other. In photosynthesis, it means the chlorophyll and phycocyanin must be near one another. In internal conversion, it means the electrode cloud must overlap the nucleus, which implies that the process usually results in emission of a K-shell electron since those innermost electrons have the highest probability of being near the nucleus.

There’s lots of interesting stuff here: How working at the border between disciplines can result in breakthroughs; how physics concepts can contribute to biology; how addressing oddball questions arising from data can lead to new breakthroughs; how quantum mechanics can influence biological processes (Newton rules biology, except when he doesn’t); how seemingly different phenomena—such as FRET imaging, photosynthesis, and nuclear internal conversion—can have underlying similarities. I wish my command of quantum mechanics was strong enough that I could explain all these resonance effects to you in more detail, but alas it is not.

Oppenheimer and General Groves
at the Trinity test site. I love
Oppie’s pork pie hat.

If you haven’t seen Oppenheimer yet, I recommend you do. Go see Barbie too. Make it a full Barbenheimer. But if you want to learn about the father of the atomic bomb’s contributions to biology, you’d better stick with From Photon to Neuron or this blog. 

 

 

The official trailer to Oppenheimer.

https://www.youtube.com/watch?v=bK6ldnjE3Y0

 

 

Photosynthesis.

https://www.youtube.com/watch?v=jlO8NiPbgrk&t=14s

The Dobson Unit

In Chapter 14 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the risk of DNA damage—and therefore cancer—caused by ultraviolet light from the sun. Figure 14.28 in IPMB presents the results of a calculation of UV dose rate, weighted for DNA damage. The caption of the figure states “the calculation assumes clear skies and an ozone layer of 300 Dobson units (1 DU = 2.69 × 10²⁰ molecule m^-2).”

The Dobson Unit, what’s that?

Rather than explaining it myself, let me quote the NASA website about ozone.

What is a Dobson Unit?

The Dobson Unit is the most common unit for measuring ozone concentration. One Dobson Unit is the number of molecules of ozone [O₃] that would be required to create a layer of pure ozone 0.01 millimeters thick at a temperature of 0 degrees Celsius and a pressure of 1 atmosphere (the air pressure at the surface of the Earth). Expressed another way, a column of air with an ozone concentration of 1 Dobson Unit would contain about 2.69 × 10¹⁶ ozone molecules for every square centimeter of area at the base of the column. Over the Earth’s surface, the ozone layer’s average thickness is about 300 Dobson Units or a layer that is 3 millimeters thick.

The Dobson Unit was named after British physicist and meteorologist Gordon Miller Bourne Dobson (1889 –1976) who did early research on ozone in the atmosphere.

Worried about climate change? The ozone story may provide some hope. When man-made chemicals such as chlorofluorocarbons, for example freon, are released into the atmosphere, they damage the ozone layer, allowing larger amounts of ultraviolet radiation to reach the earth’s surface. In the 1970s, an ozone hole developed each year over the south pole. In 1987, countries from all over the world united to pass the Montreal Protocol, which banned many ozone depleting substances. Since that time, the ozone hole has been getting smaller. This represents a success story demonstrating how international cooperation can address critical environmental hazards. Now, we need to do the same thing for greenhouse gases to combat climate change. 

 

How the ozone layer was discovered.

https://www.youtube.com/watch?v=GS0dilngPws

Don't let this happen to your planet!

https://www.youtube.com/watch?v=nCpH71npnvo

Decay Plus Input at a Constant Rate Revisited

In Chapter 2 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss the problem of decay plus input at a constant rate.

Suppose that in addition to the removal of y from the system at a rate –by, y enters the system at a constant rate a, independent of y and t. The net rate of change of y is given by

Then we go on to discuss how you can learn things about a differential equation without actually solving it.

It is often easier to write down a differential equation describing a problem than it is to solve it… However, a good deal can be learned about the solution by examining the equation itself. Suppose that y(0) = 0. Then the equation at t = 0 is dy/dt = a, and y initially grows at a constant rate a. As y builds up, the rate of growth decreases from this value because of the –by term. Finally when a – by = 0, dy/dt is zero and y stops growing. This is enough information to make the sketch in Fig. 2.13.

The equation is solved in Appendix F. The solution is

… The solution does have the properties sketched in Fig. 2.13, as you can see from Fig. 2.14.

Figure 2.13 looks similar to this figure

Sketch of the initial slope a and final value a/b of y when y(0) = 0. In this figure, a=b=1.

 And Fig. 2.14 looks like this

A plot of y(t) using Eq. 2.26, with a=b=1.

However, Eq. 2.26 is not the only solution that is consistent with the sketch in Fig. 2.13. Today I want to present another function that is consistent with Fig. 2.13, but does not obey the differential equation in Eq. 2.25.

Let’s examine how this function behaves. When bt is much less than one, the function becomes y = at, so it’s initial growth rate is a. When bt is much greater than one, the function approaches a/b. The sketch in Fig. 2.13 is consistent with this behavior.

Below I show both Eqs. 2.26 and 2.26’ in the same plot.

A plot of y(t) using Eq. 2.26 (blue) and Eq. 2.26' (yellow), with a=b=1.

The function in Eq. 2.26 (blue) approaches its asymptotic value at large t more quickly than the function in Eq. 2.26’ (yellow).

The moral of the story is that you can learn a lot about the behavior of a solution by just inspecting the differential equation, but you can’t learn everything (or, at least, I can’t). To learn everything, you need to solve the differential equation. 

By the way, if Eq. 2.26’ doesn’t solve the differential equation in Eq. 2.25, then what differential equation does it solve? The answer is

 How did I figure that out? Trial and error.

The Slide Rule

In Chapter 2 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I discuss semilog plots, where the vertical axis is marked using a logarithmic scale. In this case, a constant distance along the vertical axis corresponds to a constant multiple in the numerical value. In other words, the distance between 1 and 2 is the same as the distance between 2 and 4, which is the same as the distance between 4 and 8, and so on. Looking at a semilog plot helps the reader get a better understanding of how logarithms and exponentials work. Yet, what would be a really useful learning tool is not something readers just look at, but something that they can hold in their hands, something they can manipulate, something they can touch.

Enter the slide rule. Sixty years ago, when electronic calculators did not yet exist, the slide rule is how scientists and engineers performed calculations. I didn’t use a slide rule in school. I’m from the first generation that had access to electronic calculators. They were expensive but not prohibitively so, and we all used them. But my dad used a slide rule. He gave me his, mainly as an artifact of a bygone era. I rarely use it but I have kept it in honor of him. It was made by the Keuffel & Esser Company in New York. It is a fairly fancy one and has a variety of different scales.

First, let’s look at the C and D scales. These are marked logarithmically, just like semilog paper. In fact, if you wanted to draw you own semilog graph paper, you could take out my dad’s slide rule, hold it vertical, and mark off the tick marks on your plot axis. On dad’s slide rule, C and D are both marked logarithmically, but they can move relative to each other. Suppose you wanted to prove that the distance between 1 and 2 is the same as the distance between 2 and 4. You could slide the C scale so that its 1 lined up with the 2 on the fixed D scale. If you do this, then the 2 on the C scale really does line up with the 4 on the D scale, and the 4 on the C scale matches the 8 on the D scale. The value on the D scale is always twice the value on the C scale. When you think about it, you have just invented a way to multiply any number by 2. 

A slide rule showing how to multiply by 2.

This trick of doing multiplication isn’t just for multiplying by 2. Suppose you wanted to multiply 1.7 by 3.3. You could line the 1 on the C scale up with 1.7 on the D scale, and then look at what value on the D scale corresponds to 3.3 on the C scale. The slide rule has a handy little ruled glass window called the cursor that you can use to read the D scale accurately (if the cursor lands between two tick marks, don’t be afraid to estimate an extra significant figure based on where it is between ticks). I get 5.60. Use you calculator and you get 5.61. The slide rule is not exact (my answer was off by 0.2%) but you can get an excellent approximation using it. If my eyes weren’t so old, or if I had a more powerful set of reading glasses, I might have gotten a answer that was even closer. I bet with practice you young folks with good eyes and steady hands could routinely get 0.1% accuracy.

A slide rule showing how to multiply 1.7 by 3.3.

If you can do multiplication, then you can do its inverse: division. To calculate 8.2/4.5, move the cursor to 8.2 on the D scale, then slide the C scale until 4.5 aligns with the cursor. Then read the value on the D scale that aligns with 1 on the C scale. I get 1.828. My calculator says 1.822. When using the slide rule, you need to estimate your result to get the decimal place correct. How do you know the answer is 1.828 and not 18.28 or 0.1828? Well, the answer should be nearly 8/4 = 2, so 1.828 must be correct. Some would claim that the extra step of requiring such an order-of-magnitude estimate is a disadvantage of the slide rule. I say that even when using an electronic calculator you should make such estimates. It’s too easy to slip a decimal point somewhere in the calculation, and you always want to have a rough idea of what result you expect to avoid embarrassing mistakes. Think before you calculate! 

A slide rule showing how to divide 8.2 by 4.5.

Suppose you have a number like 5.87 and you want to know its reciprocal. You could, of course, just calculate 1/5.87. But like most scientific calculators that have a special reciprocal key, dad’s slide rule has a special CI scale that performs the calculation quickly. The CI scale is merely the mirror image of the C scale; it is designed logarithmically, but from right to left rather than from left to right. Put the cursor at 5.87 on the CI scale, and then read the value of the C scale (no sliding required). I read 1.698. I estimate that 1/5 is about 0.2, so the result must really be 0.1698. My electronic calculator says 0.1704.

A slide rule showing how to calculate the reciprocal of 5.89.

One property of logarithms is that log(x²) = 2 log(x). To calculate squares quickly use the A scale (on my dad’s slide rule the A scale is on the flip side), which is like the C or D scales except that two decades are ruled over A whereas just one is over D. If you want 15.9², put 1.59 on the D scale and read 2.53 on the A scale (again, no sliding). You know that 16² is 256, so the answer is 253. My calculator says 252.81. Not bad.

A slide rule showing how to calculate the square of 15.9.

If you can do squares, you can do square roots. To calculate the square root of 3261, place the cursor at 3.261 on the A scale. There is some ambiguity here because the A scale has two decades so you don’t know which decade to use. For reasons I don’t really understand yet, use the rightmost decade in this case. Then use the cursor to read off 5.72 on the C scale. You know that the square root of 3600 is 60, so the answer is 57.2. My calculator says 57.105. 

A slide rule showing how to calculate the square root of 3261.

There are additional scales to calculate other quantities. The L scale is ruled linearly and can be used with the C scale to compute logarithms to base 10. Other scales can be used for trig functions or powers.

I don’t recommend giving up your TI-30 for a slide rule. However, you might benefit by spending an idle hour playing around with an old slide rule, getting an intuitive feeling for logarithmic scaling. You’ll never look at a semilog plot in the same way again.

How to use a slide rule.

https://www.youtube.com/watch?v=xYhOoYf_XT0

Meeting of Minds

An episode of Meeting of Minds, with (l-r) Atilla the Hun, Emily Dickinson, host Steve Allen, Charles Darwin, and Galileo Galilei.

 

When I was a teenager, one of my favorite shows was Meeting of Minds. This television series, which aired on PBS from 1977 to 1981, featured historical figures interacting in a talk-show format. The host was the delightful comedian, musician, and television personality Steve Allen.

The episode containing the most science—and therefore most closely related to Intermediate Physics for Medicine and Biology—had as guests Charles Darwin, Galileo Galilei, Emily Dickinson, and Attila the Hun. You can watch this episode at the website for the American Archive of Public Broadcasting. I highly recommend it.

Below is an excerpt from when Darwin was discussing his voyage on the Beagle (in the video, this section starts at about 23:15).

Dickinson: How old were you when you made the trip?

Darwin: I was only 22. We set out from Plymouth on December the 27th, 1831.

Allen: A long or short voyage?

Darwin: Oh, it was five long years before I returned to England. It seems to me now that those five years constituted my real education.

This discussion took place when Darwin was discussing the controversy caused by his theory of evolution by natural selection (26:15)

Dickinson: Dr. Darwin, we know that your theories got you into the most dreadful trouble, that you were violently criticized, as was Signore Galilei. But what I cannot understand is how such common sense reasoning could have gotten you into such incredible difficulty.

Darwin: Oh my dear woman, the real trouble didn’t come about until after I presented to the world the idea that the common ancestry of all living things included man.

Galileo: Oh, how they must have howled for your blood when you said that!

I think the writers gave Galileo the best lines, like when Darwin and Galileo were discussing the dogmatism of Aristotle (38:45).

Darwin: It’s by no means a simple question as to what extent one should respect intellectual authority.

Galileo: There you are quite right. We must pay the most careful attention to what the great minds of earlier ages have discovered… But, we must never let our admiration for these great men blind us to the fact that they were only human, for their humanity means that they will inevitably fall into error at certain times.

Finally, a great soliloquy by Galileo about reason versus faith (45:50).

Galileo: There may be doubts and arguments as to the passages of scripture, problems of translation, et cetera. But there should be no room for doubt or argument about the evident facts of the physical world about us. Nature, unlike the sometimes confusingly worded scriptures, is inexorable and immutable, and does not care one jot whether her reasons and modes of operation are above or below the capacity of man’s understanding.

I like it best when the guests argue with each other (Dickinson gets so exasperated with Attila). For those of you whose interest is not science, you might enjoy listening to Dickinson read some of her poems or hear Atilla tell old war stories.

If I were Steven Allen and had to choose four guests to discuss physics in medicine and biology, who would I select? It’s tough to narrow it down to just four, but I would invite Marie Curie, Willem Einthoven, Alan Hodgkin, and Paul Lauterbur. Wouldn’t that be a fascinating discussion!  Curie could tell us how she and her husband Pierre analyzed and purified tons of ore to isolate two new elements: radium and polonium. She could also recount her experience using medical x-rays during World War I. Einthoven could describe how he recorded the first electrocardiogram, and how he balanced his education in medicine with his interest in physics. Hodgkin could explain his research with Andrew Huxley that determined how nerves work. And Lauterbur could reflect on his invention of magnetic resonance imaging. Perhaps Curie might ask Lauterbur about who really invented MRI, him or Raymond Damadian. And Einthoven might probe into who deserves the credit for the voltage clamp, Hodgkin or Kenneth Cole. And they all could compare their experiences receiving the Nobel Prize (I can just hear Curie saying “but gentlemen, how many of you have two?”) What fun.

 

I could not find the Meeting of Minds episode with Darwin and Galileo on YouTube, so I couldn’t embed the link. I did find another episode on YouTube, featuring Teddy Roosevelt, Cleopatra, Thomas Paine, and Thomas Aquinas. It’ll give you a flavor of what the show is like.

https://www.youtube.com/watch?v=hKRxZSOqAYw

The Greatest Shortcoming of the Human Race is our Inability to Understand the Exponential Function

Ten years ago yesterday, on September 7, 2013, Physicist Albert Bartlett died at the age of 90. Russ Hobbie and I mentioned Bartlett in Chapter 2 of Intermediate Physics for Medicine and Biology.

Exponential growth cannot go on forever. This fact is often ignored by economists and politicians. Albert Bartlett has written extensively on this subject. You can find several references in The American Journal of Physics and The Physics Teacher. See the summary in Bartlett (2004).

The Essential Exponential!
by Albert Bartlett.

The reference is to

Bartlett A (2004) The Essential Exponential! For the Future of our Planet. Center for Science, Mathematics & Computer Education, Lincoln

To celebrate Bartlett’s life, I’ll quote excerpts from an interview with Paul Nachman in May, 2005.

I started as an undergraduate in the fall of 1940 at Otterbein College in Westerville, Ohio. (It's a small, church-founded school, and my father was a Professor of Education there. Westerville back then was a separate town north of Columbus. Now it's been engulfed by Columbus.) In the spring of 1941, I was looking for some adventure, so I got a summer job washing dishes on an iron ore freighter on the Great Lakes. It took me several hitchhiking trips to Cleveland to get all the federal papers you need to work on the ships…

When September came along, I was having a good time, making good money, so I didn’t return to school. And that fall was Pearl Harbor. We were unloading the last cargo of iron ore for the season at the Wickwire-Spencer steel mill in Tonawanda, New York, on December 7. I’d finished cleaning up after lunch, then gone to my room and turned on the radio. I was the first person on board to hear the report...

Fortunately for all of us, Bartlett returned to college.

I said to myself, “I need to get back to college.” Writing from the boat, I applied to transfer to Colgate University in upstate New York. I was accepted, so, coming into Cleveland one day, I told the steward I was leaving to go back to college. I hitchhiked back to my home, changed from shipboard clothes to college clothes, hitchhiked up to Hamilton, New York, and started there in the fall semester of 1942.

Bartlett studied physics and math, and graduated from Colgate in 1944. Listen to how he ended up working on the Manhattan Project.

One of my professors heard that there was an address, “Box 1663,” in Santa Fe, New Mexico, where they were hiring physicists. Sounded like adventure to me, so I applied. Didn’t know what it was, and they didn't tell me and I was accepted. 

My only instructions were to appear at 109 E. Palace in Santa Fe. So, after graduation, I hitchhiked home to Ohio, and to Springfield where a friend helped me get two new International Harvester trucks from the factory. I drove them to a dealer in Oklahoma City and then hitchhiked to Amarillo. All my life I’d wanted to ride a freight train, so I hopped a freight in Amarillo to Belen, south of Albuquerque. Then I hitchhiked to Santa Fe and reported to 109 E. Palace. The lady there in the office was Dorothy McKibben. She did some paperwork and had me get on an Army bus in the alley in back. It took me off through the desert and canyons up to Los Alamos. Quite an experience! I arrived on July 18, 1944 and worked for 25 months there.”

At Los Alamos he worked on mass spectrometry of plutonium.

It wasn’t that I knew anything about mass spectrometry, but this was just at a time when the first plutonium was coming down from Hanford, and there was some indication that, in addition to the principal isotope ²³⁹Pu, there may be some ²⁴⁰Pu from an extra neutron capture in the Hanford reactors.

Now ²⁴⁰Pu has a high spontaneous fission probability, which would upset all their [bomb] calculations. So they wanted to know how much was there. They’d just requisitioned a mass spectrometer from a lab in Washington, DC, about the time I got there, and Bob Thompson, who’d been a PhD student with Al Nier at Minnesota, was setting it up. Bob took me on me sort of as an apprentice and took a real interest in me, telling me what I needed to study, giving me a stack of reprints to read, etc. He was very helpful. So we made the first measurements of the isotopic constitution of plutonium coming out of the reactors.

In 1946 he went to Harvard for graduate study in physics. His PhD project was to build

… a beta-ray [electron] spectrometer. I finished at Harvard and came out to Colorado in the late summer of 1950. I’ve been here ever since.

By Colorado, he meant the University of Colorado in Boulder. I interviewed at Boulder for graduate school around 1982. I can’t remember if I met Bartlett. I hope I did.

Bartlett was primarily focused on physics education. He was a leader in the American Association of Physics Teachers.

In 1978, I was national President of the American Association of Physics Teachers [AAPT]. I had four years in the AAPT presidential sequence vice-president, president-elect, president, and past president with duties in each of those offices. In ’78 I was the President, so I was quite involved with physics education, and I think that was why I was named an APS Fellow.

Bartlett is best known for his talk on exponential growth and the environment, which he gave over 1700 times (watch in on the YouTube videos below). Here is how it all got started.

Well, during all the uprising on the campus, there was a surge of student interest in the environment, and I had been slowly coming to the realization that students and other people didn’t have an understanding of the arithmetic of compound interest. So I started putting some notes together, and in September of 1969 the undergraduate pre-med honor society asked if I could speak on something or other at one of their meetings. I’d known many of these kids from the previous year when I was lecturing in the pre-med beginning physics course, so I put these notes together and on September 19, 1969 talked to them about growth and the problems of growth.

It didn’t have anything like the scope of today’s presentation. But, fortunately, I kept my notes and the next year I had two or three more invitations. It evolved as I became more interested. Finally in '78 or '79, I gave the talk 131 times. It was sort of like a Hubbert peak! It went down after that, but instead of going to zero, it’s leveled off at about 40 times a year.

With climate change becoming the major environmental issue of our time, we must all remember Bartlett’s famous quote:

The greatest shortcoming of the human race is our inability to understand the exponential function.

This inability is all the more reason to study Chapter 2 in IPMB, about exponential growth and decay. The survival of our species may depend on us somehow learning to understand exponential growth and its limitations.

A final reason to celebrate Bartlett is that this year, 2023, is the 100th anniversary of his birth: March 21, 1923. Happy 100th birthday, Albert Bartlett. We need you now more than ever!

The Most Important Video You Will Ever See (Part 1)

The Most Important Video You Will Ever See (Part 2)

 

 The Most Important Video You Will Ever See (Part 3)

 

The Most Important Video You Will Ever See (Part 4)

 The Most Important Video You Will Ever See (Part 5)

 

 

The Most Important Video You Will Ever See (Part 6)

 

 

The Most Important Video You Will Ever See (Part 7)

 

 

The Most Important Video You Will Ever See (Part 8)

 

Al Bartlett discusses population growth, climate change, energy, and consumption.

Is Japan's Plan to Release Radioactive Water into the Pacific Ocean Safe?

When listening to NBC Nightly News on August 24, I heard Lester Holt discuss Japan’s plan to release into the Pacific Ocean treated wastewater from the Fukushima nuclear power plant, the reactor that melted down after the 2011 earthquake and tsunami. Apparently this plan has caused an uproar, with Russia banning the import of seafood from Japan and residents of South Korea staging protests.

Is there a significant risk to dumping this treated water into the ocean? I will base my analysis on the recently published IAEA Comprehensive Report on the Safety Review of the ALPS-Treated Water at the Fukushima Daiichi Nuclear Power Station.

Two years ago, Japan developed a plan for the handling of Advanced Liquid Processing System (ALPS) treated water at the Fukushima Nuclear Power Station, which included a proposal to release the water into the ocean. Japan then asked the International Atomic Energy Agency (IAEA) to review the safety of their plan. The IAEA Director General established a task force to conduct this review, consisting of independent experts from all over the world (including Russia and South Korea). The task force recently published its report, whose purpose is “to present the IAEA’s final conclusions and findings of the technical review to assess whether the planned operation to discharge the ALPS treated water into the Pacific Ocean over the coming decades is consistent with relevant international safety standards.” The task force concluded that “the approach to the discharge of ALPS treated water into the sea… [is] consistent with relevant international safety standards” and that “the discharge of the ALPS treated water… will have a negligible radiological impact on people and the environment.”

In Chapter 16 of Intermediate Physics for Medicine and Biology, Russ Hobbie and I analyze the risk of radiation. We write

One way to express risk is to compare medical doses to the natural background. We are continuously exposed to radiation from natural sources. These include cosmic radiation, which varies with altitude and latitude; rock, sand, brick, and concrete containing varying amounts of radioactive minerals; the naturally occurring radionuclides in our bodies such as ¹⁴C and ⁴⁰K; and radioactive progeny from radon gas.

The effective dose of radiation is measured in sieverts, or more conveniently millisieverts (mSv). The typical effective dose from natural sources is about 3 mSv per year. What is the dose expected from releasing Japan’s radioactive water into the Pacific? According to the IAEA report, it is in the range from 0.000002 to 0.00004 mSv per year. So, we constantly are exposed to about 3 mSv/year of radiation and now we will experience 3.00004 mSv/year. The risk is negligible.

According to Table 16.6 in IPMB, flying in a plane at 40,000 feet—where cosmic ray exposure is increased—is 0.007 mSv per hour. That means the extra dose caused by the release of radioactive water is approximately equal to the extra dose received during 20 seconds of airplane flight. 

The value of 0.00004 mSv/year assumes the water is slowly released as planned. What if there is an accident? The IAEA report examined two accident scenarios and concluded that the upper limit of exposure is 0.01 mSv per accident. In other words, if three of the holding tanks accidentally dump all of their treated water into the Pacific at one time, your dose would be less than one percent of your yearly dose from natural sources. 

Another way to look at it the risk is to analyze the amount of tritium released. The treatment of the water before release removes most of the radioactive contaminates except tritium, which is the radioactive isotope hydrogen-3. Tritium is usually found as part of a water molecule, so it is extraordinarily difficult to separate it form normal water. Tritium is constantly being created in our atmosphere by cosmic rays colliding with nitrogen. About 100,000 TBq is produced each year. A becquerel (Bq) is one nuclear decay and tera- (T) is the metric prefix for 1,000,000,000,000. How much tritium will be released each year from Japan’s wastewater? 22 TBq. In other words, the amount of tritium released is about 5000 times less than the amount naturally produced. Once the released water is diluted and mixed with ocean water, the increase in tritium concentration will be insignificant.

My conclusion is that releasing the treated water into the ocean is safe, with a large margin of safety. Russia and South Korea can relax. Lester Holt, I love ya, but you really gotta read the IAEA report more carefully. 

There are plenty of things we all should worry about (just listen to the rest of the news report in the video below). The release of Japan’s wastewater into the ocean is not one of them. 

NBC Nightly News with Lester Holt, August 24, 2023. See 14:30–16:40 for the report on Japan’s plan to release radioactive water into the ocean.

 https://www.youtube.com/watch?v=pdFrCE3VzVQ