## Hva skjer i reaktoren? (Firefaktorformel)

Denne ukens formelfredag MÅ jo bli en liten oppsummering av forelesningen jeg holdt i nukleær teknologi tidligere i dag: Firefaktorformelen (som ved en feil først ble skrevet Fire4faktorformelen nå - og det er vel nesten sånn jeg burde fortsette å skrive den 😛 ). Vi bretter opp ermene, selv om det er fredag, og går rett på sak!

- oppskrift -

Firefaktorformelen er, som det vel nesten sier seg selv, en formel som består av fire faktorer - altså fire forskjellige tall/verdier som ganges sammen (faktorer er ting som ganges sammen). Den er enkel og grei på formen, og ikke vanskelig å bruke i det hele tatt, og den ser sånn ut:

og med ord så blir det k uendelig $$(k_\infty)$$ er lik epsilon $$(\epsilon)$$ ganget med p ganget med f ganget med eta T $$(\eta_T)$$, for det står et usynlig gangetegn mellom faktorene, som man vanligvis ikke skriver. Jeg har faktisk ikke vært konsekvent på om jeg skriver gangetegn eller ikke her på bloggen innser jeg, for forrige ukes strekning og fart og tid skrev jeg med gangetegn, mens formelfredag for to uker siden, som handlet om Newtons andre lov, skrev jeg uten gangetegn... Vel vel, da er det i alle fall forklart, og det er lov å skrive uten å ta med gangetegnet 🙂

- hva det betyr -

På venstre siden av likhetstegnet står k uendelig, og dette kalles for nøytron-multiplikasjonsfaktoren (for en uendelig stor reaktor). For å holde tunga rett i munnen: nøytron-multiplikasjonsfaktoren forteller om det blir flere eller færre nøytroner i en reaktor, så det er altså forholdet mellom hvor mange nøytroner som fins etter den nåværende generasjonen med fisjon sammenliknet med hvor mange det var i forrige generasjon.

Hvis k er større enn 1 så betyr det at det skjer mer og mer fisjoner i brenselet, og reaktoren løper løpsk. Hvis k er akkurat 1 (som den skal) så er reaktoren kritisk, og det betyr at den er balansert og alt er fint og flott, og det er like mye fisjon som skjer hele tiden. Hvis k er mindre enn 1 så betyr det at det skjer mindre og mindre fisjon i brenselet, og hele kjedereaksjonen slutter og reaktoren skrur seg av.

På høyre side av likhetstegnet står det først $$\epsilon$$, som er hvor mange nøytroner som vil gå rett og gi rask fisjon (fast fission factor), og dermed flere nøytroner totalt sett. Neste  faktor er p, som er hvor mange nøytroner som blir spist opp av brenselet mens de egentlig skal bremses ned (resonance escape probability), så her blir det færre nøytroner. Faktor nummer tre er f, som forteller hvor mange termiske nøytroner som faktisk blir spist opp - så selv om nøytronene har overlevd til den energien som gir høyest sannsynlighet for fisjon så vil allikevel en god del bli spist opp i ikke-brensel (thermal utilization). Til slutt er det $$\eta_T$$, som forteller hvor mange nøytroner man får for hvert nøytron som treffer en spaltbar kjerne, altså som treffer en kjerne i det som faktisk er brensel.

- fremgangsmåte -

Hvis vi starter med 1000 nøytroner, så skal det fortsette å være 1000 nøytroner totalt etter hver eneste generasjon med fisjoner i brenselet.

Eta kan feks være 1.04. Det betyr at det blir 1000 nøytroner ganget med 1.04 = 1040 nøytroner. Videre kan p være 0.8, som gjør at av de 1040 nøytronene er det bare 1040*0.8 = 832 som overlever det å bli bremset ned til lav energi. De andre blir "spist opp" av uran-238 (hovedsakelig) på veien. Deretter kan f være 0.799, som betyr at 832*0.799 = 655 - altså at det er 655 nøytroner som faktisk gir fisjon i brenselet. De andre nøytronene (832-655 = 167) blir "spist opp" av kjølevæske og kontrollstaver og uran-238 (forskjellen fra den forrige faktoren er at nå er det snakk om de nøytronene som har fått riktig energi, mens den forrige faktoren handler om hva som skjer på veien fra høy energi til riktig, lav energi), som altså ikke fisjonerer. Den siste faktoren er $$\eta_T$$, som forteller hvor mange nøytroner som kommer ut for hvert nøytron som går inn i en fissil kjerne (altså uran-235). $$\eta_T$$ er faktisk ikke det det samme som hvor mange nøytroner man får fra hver eneste fisjon, for $$\eta_T$$ tar også med i beregningen at en liten del av de nøytronene som treffer uran-235-kjernen vil bli spist opp, og noen vil gjøre andre ting. Hvis $$\eta_T$$ = 2.02 blir det 655*2.02 = 1323 nøytroner.

1323 er åpenbart mer enn de 1000 som var til å begynne med, så det kan virke som om de tallene jeg har satt opp gir en kjedereaksjon som løper løpsk. MEN! Firefaktorformelen tar ikke med en siste, viktig faktor - nemlig hvor mange nøytroner som forsvinner ut av reaktoren (det er ikke så lett å passe på alle nøytronene hele tiden). Det er det som ligger i $$k_\infty$$, altså en uendelig stor reaktor - for hvis reaktoren er uendelig stor vil jo heller ingenting noensinne kunne forsvinne ut av den. I vikeligheten er selvsagt ingen reaktor uendelig stor, og man må derfor også ta med at en viss del av nøytronene som produseres vil forsvinne.

Hvis sannsynligheten for at nøytronene skal bli i reaktoren er 0.7559 (det vil si 75.59%), eller, sagt på en annen måte 24.41% av alle nøytronene forsvinner ut av reaktoren, og da er de bare tapt :/ Når vi trekker fra de 24.41% som forsvinner, så sitter vi igjen med like mange nøytroner som vi startet med, og kjedereakjsonen er balansert og kritisk og veldig fin ♥

Bildet under viser nettopp forskjellen på en kritisk kjedereaksjon til høyre - altså at én fisjon i gjennomsnitt gir én ny fisjon, mens det er en overkritisk kjedereaksjon til venstre - altså at én fisjon gir feks tre nye fisjoner og hver av dem gir tre nye igjen...

PS: Et kjernekraftverk kan aldri eksplodere som en atombombe! Altså, den kjedereaksjonen som skjer i et kjernevåpen kan ikke skje i et kjernebrensel 🙂

PPS: Goood helg nydelige mennesker ♥♥♥

## Ten facts about depleted uranium 1

As we were approaching the Tenerife airport yesterday, I suddenly remembered something...
The thing is, I have this weird fascination for accidents and catastrophes (Titanic, bombings of Hiroshima and Nagasaki, the Chernobyl accident, and more or less all accidents from "air crash investigation ") - which is probably one of the main reasons I was interested in nuclear physics in the first place. If you're like me, you might know which thing, or accident, I came to think about as we were approaching the airport? It was of course the Tenerife accident of March 1977, involving two Boeing-747, that crashed at the runway, killing close to 600 people. If you're weird like me, you probably don't think I'm completely crazy for googling the accident. (If you're not like me, you might think I'm insane for reading all I could find about the deadliest air crash ever, just before I'm about to go on a six hours flight :v )
First I found a very interesting and well written article, but after I had read this, and still wanted more, I kept scrolling, and suddenly I saw the two words depleted uranium. I don't think it was from the most serious web page ever, but I was inspired by it to make ten facts about this mysterious material - check fact number 10 for why the Tenerife air crash and depleted uranium have anything to do with each other:

1. depleted uranium is what you get when you take natural uranium, and you enrich it to get enriched uranium for nuclear fuel - the "waste" from this process is the depleted uranium (natural uranium minus enriched uranium equals depleted uranium, to sort of make into an equation <3) reason why it's called "depleted" is that it's depleted in the fissile uranium-235
2. natural uranium is made by uranium-238, uranium-235, and uranium-234. The uranium-238 isotope makes up 99.275%, uranium-235 is 0.72%, and uranium-234 is just 0.0054%. Depleted uranium is made up by typically 99.799% uranium-238, 0.2% uranium-235, and 0.001% uranium-234
3. depleted uranium is often called just DU
4. it's the least radioactive kind of uranium: depleted uranium is less radioactive than natural uranium - meaning it's close to not radioactive at all. Uranium-238 has an activity of 12 445 Bequerels per gram, uranium-235: 80 011 Bequerels per gram, and uranium-234: 231 million Bequerels per gram. The total activity of natural uranium is therefore: 25 280 Bequerel from 1 gram (meaning that 25 280 atoms of the uranium - either 234, 235, or 238 is changed into another atom every second :D), and the activity of depleted uranium is about half the activity: typically 14 600 Bequerels per second. (Don't be fooled by long halflifes - the longer the halflife, the less radioactivity... Activity/radioactivity sort of tells us how fast a material is turning into something stable: if the radioactivity is very high, the halflife is short. If it's very very low, the halflife is long. Uranium-238 has a halflife of 4.5 billion years, and is not at all very radioactive.)
5. the gamma dose rate from a 30 mm DU-bullet (of 271 grams) at a distance of 1 m is 7 nano sieverts per hours, which is almost not distinguishable from the normal background radiation of typically 100 nano sieverts per hour. If you take 10 kg of DU and disperse it over 1000 m2 the result is a gamma dose rate of 4 micro sieverts per year (the average background radiation from gamma in Norway is 0.5 milli sieverts)
6. DU is extremely dense, and therefore very heavy. Natural uranium is already a metal of high density, with 18.9 g/cm3, and DU is even more dense: 19.1 g/cm3 - making it almost 70% denser than lead
7. because of the extreme density, it's used as ammunition; since a projectile made from DU has a bigger kinetic energy than if it were made by lead, and therefore it will penetrate or destroy almost anything. Also, if a DU bullet hits a tank, all the energy that it's carrying will turn it into dust, and the heat generated will make it burn. If you're in a tank that's hit by a DU projectile - it's not exactly the radioactivity you should fear...
8. DU is actually the best kind of shielding you can make to protect yourself against gamma- or X-rays. It's even better than lead, since uranium has 92 protons in the nucleus, compared to only 82 in lead. (You could also shield with natural uranium, but since natural uranium has more of the uranium-235 isotope than depleted uranium, and 235 is more radioactive than 238 and DU, you would rather use DU than natural uranium)
9. uranium (thus also depleted uranium) is a heavy metal, like lead, and this fact is the main reason it's not very healthy - not the radioactivity. You take natural uranium, and make into something that's about half as radioactive as it already was. It's not like you make a new radioactive material.
10. depleted uranium is also used as counterweight in airplanes like the Boeing-747; that carries around 250 kg of DU. I didn't know this until I started reading all I could find about the 1977 Tenerifie aircrash. I definitely learned something new, and now I want to learn more about counterweights 🙂
Luckily we got home safely after a great week of vacation, and I think I'm ready for a couple of very busy months. I've made a nice plan for this week, that includes talking about cold fusion on the radio tomorrow. Sorry I haven't been "here" last week, but I needed the vacation, and Alexandra needed her mother to be there, on vacation with her, and not on the cell or the computer all the time...:)

## References, figures, and references

...and figures.

And tables!

FML.
No, I'm joking, obviously, but my arms and my back hurt, and my head feels like it weighs a ton. And my eyes are dry and sore. And I'm going back and forth with respect to how to best represent my data and my results - and what to put in this article, and what to put in the next article (and I do remember, very well, that I was accused of self plagiarism one and a half year ago, and I'm of course very scared that someone will accuse me of something like this again, unless I'm extremely careful...:/)
I guess this is #phdlife <3

## Facts on Friday (we pretend Monday = Friday) – EXPERIMENTS! 4

Since I wrote about my feelings about programming on Thursday, I got some comments and questions about how and why; which can be totally ok, but also a little annoying if it's more like "why on earth are you so stupid you're trying to do anything in C++" (no one said exactly that, it's just an example of a not very constructive comment). Like my friend, Anders (not my boyfriend, but my friend who is a boy - haha), said: "With programming you can do everything! (Except for saying out load which language you are using without someone telling you it's wrong.)"
Telling me stuff like "you have to hate yourself for choosing C++" is not exactly helping me (or anyone really), right? I didn't wake up one day and say to my self "hey, I think I want to program C++ for no reason what so ever - just because I enjoy feeling stupid". I need C++. So it's a little bit like telling your kid who is doing his/her algebra homework "you must really enjoy feeling stupid since you're doing this algebra stuff - you should work on statistics instead".
I love getting constructive comments or critique, but some comments are just making me feel more stupid than before (like: not only am I not managing the programming stuff, I'm also an idiot for trying to learn what I am learning...).
So I thought, today I want to give you ten FACTS about experiments and data analysis here at the nuclear physics group in Oslo - which is the main reason why I need any knowledge of programming these days. This is probably the geekiest (and perhaps most "technical") facts post I've had so far...but sometimes you have to be a little geeky, right? 😉
1. The material we want to study can be almost anything - for example uranium, gold, nickel, molybdenum, iron, dysprosium, thorium or plutonium (these are just some examples of what we have experimented with the last couple of years)
2. We make a tiny foil - a target - from the material (almost the size of a small coin), and put this inside all of our detectors
3. There are always at leas two types of detectors for the experiments: Sodium Iodide detectors (they measure gamma rays), and Silicon detectors (they measure particles)
4. The Sodium Iodide detectors are called CACTUS (cause it really looks like a cactus) <3
5. Sometimes we use more detectors than the gamma detectors (CACTUS) and the particle detectors - for example fission detectors (we used that for my uranium experiment, since uranium-233 fissions like crazy 😛 )
6. To study the nuclei in the material we bombard the target with tiny particles; protons, deuterons (a proton and a neutron), helium-3 (two protons and one neutron), or helium-4 (two protons and two neutrons - same as an alpha particle 😀 )
7. When a particle hits a nucleus in our target material, the nucleus gets some extra energy (sort of like it gets heated); then a particle goes out (it can be the same that went in, or it can be another one), and the target nucleus cools again, by sending out gamma radiation
8. The different detectors will detect the different kind of stuff that comes out from the reaction in the target: the gamma detectors detect the gammas, the particle detectors detect the particles (protons, deuterons, helium-3, or alphas), and the fission detectors detect fission - the detection of all these thing are what we talk about as our data
9. Data from the experiments we are performing in Oslo (like my uranium experiment) is typically 10-100 Giga Bytes - so it's kind of a lot
10. To sort all of these data we need codes/programs that go through everything and checks if there for example was a particle and a gamma that came out of the target at the same time, or maybe it was a particle and a gamma and a fission product, and what were the energie
s of all this; the particles and the gammas - on the lucky side I don't have write theses sorting codes from scratch, on the other side I have to try to understand someone else's code and logic, which is not always very easy (when I don't understand I'm always sure it's because I'm stupid :/ )
- CACTUS <3 -
The sorting codes, and everything else I'm working on is written in C++, and that's the reason why that's the language I'm working on.
Happy Monday to everyone!

## Obsessing…

Monday!

Meaning another week with my plot... Obsessing about my plot. Trying to make it just perfect. Try different colours. Different styles. Obsess - science style.
On Friday I was actually thinking that this is it, that I was finished with this part of the data analysis; but then, today, I realised that other people have done similar things (analysed other uranium nuclei, for example), and that they have put five of those black pumps in the plot, instead of just four - so now I'm thinking about doing the same thing.
As you can see I've added more colours to it now; there's another, lighter pink colour, a yellow-orange'ish colour, and the uranium-235 is bright green - since someone suggested that as a colour 🙂 Maybe you have suggestions for the black bumps? They don't have to be black...;)

-------------------------------
Right now I'm having a glass of wine with supervisor Jon - he's here for the week, and in addition to obsessing about this plot, I've shown him where I am in the entire analyse thing. We looked at a couple of other plots too today, and he said that there's definitely a cool paper in there...:D (Of course we don't know for sure yet, but I choose to be optimistic <3 ) If you follow me on Snapchat (I'm sunnivarose, of course), you've seen the plot that Jon was so excited about.

## kPink+7

Remember my plot from yesterday? And how happy and proud I was because I managed to make labels for the different data?
Well, today I learned (from Gry - thank you, sweetie <3) how to make it pink - and by my self I found out how to make it the exact right kind of pink. It's called kPink+7 <3<3<3, and it's just perfect, and if you think that I'm not "brave" enough to use this colour for my uranium data in a scientific article, you're wrong 😉
Yeah, and also I did the tweaking of the data points as I also talked about yesterday (I didn't spend all day on making pink data points :P)
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Speaking of pink; tomorrow I'm going to be a guest at God Morgen Norge, together with Kathrine Aspaas, who has just written a book called Rosa er den nye pønken - tune in between nine and ten (I'm guessing something like nine thirty, but I'm not 100% sure).
PS: What other kind of colours should I use in the plot?

## Data, data, and more data

Today I've spent time at the EXFOR database - hate it and sort of love it at the same time...
So far it's the "worst" database I've visited, but so far it has also given me what I've needed *mixedfeelings*.
Then I've worked on my strength function plot, which is starting to look like something now. Tomorrow I hope to tweak it so that it will be ready for my next article 😀  #phdlife

Here are some details of today's plot:

//this may sound silly; but I was so proud of my self when I managed to make these labels (no, I do not love ROOT - yet) 😛

//shapes <3
//this has to be fixed - the slope of the square points needs to be more in line with the two sets of triangles (task of tomorrow!)

## Pure joy!

Good morning everyone <3 Day two of this California/Berkeley trip has just started, and so far I'm very happy 🙂
Yesterday I "finished" the first part of the uranium analysis (which is to find the nuclear level density of uranium-234) - that I wrote about in my last blog post - and started the second part of the analysis (which is to find the gamma ray strength function of uranium-234). The picture above show the very first result of my gamma ray strength data (the squares - both black and white) plotted together with different data from the big nuclear data bases. When I wrote "plot" and this appeared I actually screamed with excitement and joy, and hugged Cecilie, who was sitting next to me and helping me, because it looks soooo pretty - even before I've started to "tweak" my data to fit with the ones from the data bases (the ones on the right side of the plot - the little triangles).
The goal of this trip is btw to put these two properties of the nucleus (the nuclear level denisty and the gamma ray strength function) into simulations of different reactors (that uses thorium based fuel) and see if they affect the results of the simulations - when we compare to standard simulations where we don't do anything about these nuclear properties 🙂 *excited*
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Below are a couple of pictures from yesterday and today. The first one, of Anders, is probably more like what you would imagine when I say "pure joy"...;) He has just rented a nice car and is on his way to Palo Alto as we speak - he is also excited. (Actually kind of wish i could go with him, but I'm on my way to the lab now, with Cecilie - and that will of course also be fun...but in a quite different way 😛 )

beautiful morning at Berkeley campus
cutest squirrel at Berkeley campus

Cecilie and Darren discussion something important (I'm guessing 😉 ) at Jupiter, where we had dinner yesterday - and the day before, when we'd just arrived

Jupiter <3

Jupiter <3

## Berkeley baby! 2

It's official: Cecilie (my fantastic and talented colleague) and I are going to Berkeley, one week in August!!!
It is of course for working (but who doesn't want to go to Berekely and work there, huh?!?), so the trip basically takes away (big parts of) my summer vacation, since I have to do a lot of preparations before we go - or else I have really no reason to go, since it wont help to go there unless I have my results that I need to get more results 😛 On the other hand, this trip will (hopefully) enable me to write my third paper, and if so, I'll be a GIANT  LEAP (like, really) closer to my degree, so I think losing a summer vacation will definitely be worth it!
I have some plans for that third paper (article) that I'm not yet ready to share with you - but I'll do it later, when I know more about how it will go...;)

We're flying with Norwegian, directly from Oslo to Oakland (which is even closer to Berkeley that San Francisco - where we normally fly to), and it will be so nice not to change flights somewhere. Also I'm excited about flying Norwegian on such a long-distance flight - wonder how it will be...:)

## Collapse

I'm dead tired right now... After I held my talk yesterday (outfit above; trying to "be me" but just enough "conservative" at the same time) I felt like I just collapsed (I managed to take part in the conference dinner, luckily 😛 ), and this morning I just slept through my alarm - which never happens, except maybe if my body is trying to tell me a needed a couple of extra hours sleep. I've been really stressed about the talk yesterday, and the (preliminary) results that I showed was finished on Wednesday afternoon. Being so "last minute" didn't exactly feel great, and that was probably one reason why I was so nervous.
It has been a great week though; and even if I really  just want to go home now, and go to sleep, I'm going out with all my great nuclear physicist colleagues from all over the world <3
Wishing everyone a great Friday and a great (long) weekend!
(from my snap chat story - follow me at sunnivarose ;))
- in action -