More on Web3 & Crypto
Vitalik
4 years ago
An approximate introduction to how zk-SNARKs are possible (part 2)
If tasked with the problem of coming up with a zk-SNARK protocol, many people would make their way to this point and then get stuck and give up. How can a verifier possibly check every single piece of the computation, without looking at each piece of the computation individually? But it turns out that there is a clever solution.
Polynomials
Polynomials are a special class of algebraic expressions of the form:
- x+5
- x^4
- x^3+3x^2+3x+1
- 628x^{271}+318x^{270}+530x^{269}+…+69x+381
i.e. they are a sum of any (finite!) number of terms of the form cx^k
There are many things that are fascinating about polynomials. But here we are going to zoom in on a particular one: polynomials are a single mathematical object that can contain an unbounded amount of information (think of them as a list of integers and this is obvious). The fourth example above contained 816 digits of tau, and one can easily imagine a polynomial that contains far more.
Furthermore, a single equation between polynomials can represent an unbounded number of equations between numbers. For example, consider the equation A(x)+ B(x) = C(x). If this equation is true, then it's also true that:
- A(0)+B(0)=C(0)
- A(1)+B(1)=C(1)
- A(2)+B(2)=C(2)
- A(3)+B(3)=C(3)
And so on for every possible coordinate. You can even construct polynomials to deliberately represent sets of numbers so you can check many equations all at once. For example, suppose that you wanted to check:
- 12+1=13
- 10+8=18
- 15+8=23
- 15+13=28
You can use a procedure called Lagrange interpolation to construct polynomials A(x) that give (12,10,15,15) as outputs at some specific set of coordinates (eg. (0,1,2,3)), B(x) the outputs (1,8,8,13) on thos same coordinates, and so forth. In fact, here are the polynomials:
- A(x)=-2x^3+\frac{19}{2}x^2-\frac{19}{2}x+12
- B(x)=2x^3-\frac{19}{2}x^2+\frac{29}{2}x+1
- C(x)=5x+13
Checking the equation A(x)+B(x)=C(x) with these polynomials checks all four above equations at the same time.
Comparing a polynomial to itself
You can even check relationships between a large number of adjacent evaluations of the same polynomial using a simple polynomial equation. This is slightly more advanced. Suppose that you want to check that, for a given polynomial F, F(x+2)=F(x)+F(x+1) with the integer range {0,1…89} (so if you also check F(0)=F(1)=1, then F(100) would be the 100th Fibonacci number)
As polynomials, F(x+2)-F(x+1)-F(x) would not be exactly zero, as it could give arbitrary answers outside the range x={0,1…98}. But we can do something clever. In general, there is a rule that if a polynomial P is zero across some set S=\{x_1,x_2…x_n\} then it can be expressed as P(x)=Z(x)*H(x), where Z(x)=(x-x_1)*(x-x_2)*…*(x-x_n) and H(x) is also a polynomial. In other words, any polynomial that equals zero across some set is a (polynomial) multiple of the simplest (lowest-degree) polynomial that equals zero across that same set.
Why is this the case? It is a nice corollary of polynomial long division: the factor theorem. We know that, when dividing P(x) by Z(x), we will get a quotient Q(x) and a remainder R(x) is strictly less than that of Z(x). Since we know that P is zero on all of S, it means that R has to be zero on all of S as well. So we can simply compute R(x) via polynomial interpolation, since it's a polynomial of degree at most n-1 and we know n values (the zeros at S). Interpolating a polynomial with all zeroes gives the zero polynomial, thus R(x)=0 and H(x)=Q(x).
Going back to our example, if we have a polynomial F that encodes Fibonacci numbers (so F(x+2)=F(x)+F(x+1) across x=\{0,1…98\}), then I can convince you that F actually satisfies this condition by proving that the polynomial P(x)=F(x+2)-F(x+1)-F(x) is zero over that range, by giving you the quotient:
H(x)=\frac{F(x+2)-F(x+1)-F(x)}{Z(x)}
Where Z(x) = (x-0)*(x-1)*…*(x-98).
You can calculate Z(x) yourself (ideally you would have it precomputed), check the equation, and if the check passes then F(x) satisfies the condition!
Now, step back and notice what we did here. We converted a 100-step-long computation into a single equation with polynomials. Of course, proving the N'th Fibonacci number is not an especially useful task, especially since Fibonacci numbers have a closed form. But you can use exactly the same basic technique, just with some extra polynomials and some more complicated equations, to encode arbitrary computations with an arbitrarily large number of steps.
see part 3
Sam Bourgi
3 years ago
NFT was used to serve a restraining order on an anonymous hacker.
The international law firm Holland & Knight used an NFT built and airdropped by its asset recovery team to serve a defendant in a hacking case.
The law firms Holland & Knight and Bluestone used a nonfungible token to serve a defendant in a hacking case with a temporary restraining order, marking the first documented legal process assisted by an NFT.
The so-called "service token" or "service NFT" was served to an unknown defendant in a hacking case involving LCX, a cryptocurrency exchange based in Liechtenstein that was hacked for over $8 million in January. The attack compromised the platform's hot wallets, resulting in the loss of Ether (ETH), USD Coin (USDC), and other cryptocurrencies, according to Cointelegraph at the time.
On June 7, LCX claimed that around 60% of the stolen cash had been frozen, with investigations ongoing in Liechtenstein, Ireland, Spain, and the United States. Based on a court judgment from the New York Supreme Court, Centre Consortium, a company created by USDC issuer Circle and crypto exchange Coinbase, has frozen around $1.3 million in USDC.
The monies were laundered through Tornado Cash, according to LCX, but were later tracked using "algorithmic forensic analysis." The organization was also able to identify wallets linked to the hacker as a result of the investigation.
In light of these findings, the law firms representing LCX, Holland & Knight and Bluestone, served the unnamed defendant with a temporary restraining order issued on-chain using an NFT. According to LCX, this system "was allowed by the New York Supreme Court and is an example of how innovation can bring legitimacy and transparency to a market that some say is ungovernable."
Ajay Shrestha
2 years ago
Bitcoin's technical innovation: addressing the issue of the Byzantine generals
The 2008 Bitcoin white paper solves the classic computer science consensus problem.
Issue Statement
The Byzantine Generals Problem (BGP) is called after an allegory in which several generals must collaborate and attack a city at the same time to win (figure 1-left). Any general who retreats at the last minute loses the fight (figure 1-right). Thus, precise messengers and no rogue generals are essential. This is difficult without a trusted central authority.
In their 1982 publication, Leslie Lamport, Robert Shostak, and Marshall Please termed this topic the Byzantine Generals Problem to simplify distributed computer systems.
Consensus in a distributed computer network is the issue. Reaching a consensus on which systems work (and stay in the network) and which don't makes maintaining a network tough (i.e., needs to be removed from network). Challenges include unreliable communication routes between systems and mis-reporting systems.
Solving BGP can let us construct machine learning solutions without single points of failure or trusted central entities. One server hosts model parameters while numerous workers train the model. This study describes fault-tolerant Distributed Byzantine Machine Learning.
Bitcoin invented a mechanism for a distributed network of nodes to agree on which transactions should go into the distributed ledger (blockchain) without a trusted central body. It solved BGP implementation. Satoshi Nakamoto, the pseudonymous bitcoin creator, solved the challenge by cleverly combining cryptography and consensus mechanisms.
Disclaimer
This is not financial advice. It discusses a unique computer science solution.
Bitcoin
Bitcoin's white paper begins:
“A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution.” Source: https://www.ussc.gov/sites/default/files/pdf/training/annual-national-training-seminar/2018/Emerging_Tech_Bitcoin_Crypto.pdf
Bitcoin's main parts:
The open-source and versioned bitcoin software that governs how nodes, miners, and the bitcoin token operate.
The native kind of token, known as a bitcoin token, may be created by mining (up to 21 million can be created), and it can be transferred between wallet addresses in the bitcoin network.
Distributed Ledger, which contains exact copies of the database (or "blockchain") containing each transaction since the first one in January 2009.
distributed network of nodes (computers) running the distributed ledger replica together with the bitcoin software. They broadcast the transactions to other peer nodes after validating and accepting them.
Proof of work (PoW) is a cryptographic requirement that must be met in order for a miner to be granted permission to add a new block of transactions to the blockchain of the cryptocurrency bitcoin. It takes the form of a valid hash digest. In order to produce new blocks on average every 10 minutes, Bitcoin features a built-in difficulty adjustment function that modifies the valid hash requirement (length of nonce). PoW requires a lot of energy since it must continually generate new hashes at random until it satisfies the criteria.
The competing parties known as miners carry out continuous computing processing to address recurrent cryptography issues. Transaction fees and some freshly minted (mined) bitcoin are the rewards they receive. The amount of hashes produced each second—or hash rate—is a measure of mining capacity.
Cryptography, decentralization, and the proof-of-work consensus method are Bitcoin's most unique features.
Bitcoin uses encryption
Bitcoin employs this established cryptography.
Hashing
digital signatures based on asymmetric encryption
Hashing (SHA-256) (SHA-256)
Hashing converts unique plaintext data into a digest. Creating the plaintext from the digest is impossible. Bitcoin miners generate new hashes using SHA-256 to win block rewards.
A new hash is created from the current block header and a variable value called nonce. To achieve the required hash, mining involves altering the nonce and re-hashing.
The block header contains the previous block hash and a Merkle root, which contains hashes of all transactions in the block. Thus, a chain of blocks with increasing hashes links back to the first block. Hashing protects new transactions and makes the bitcoin blockchain immutable. After a transaction block is mined, it becomes hard to fabricate even a little entry.
Asymmetric Cryptography Digital Signatures
Asymmetric cryptography (public-key encryption) requires each side to have a secret and public key. Public keys (wallet addresses) can be shared with the transaction party, but private keys should not. A message (e.g., bitcoin payment record) can only be signed by the owner (sender) with the private key, but any node or anybody with access to the public key (visible in the blockchain) can verify it. Alex will submit a digitally signed transaction with a desired amount of bitcoin addressed to Bob's wallet to a node to send bitcoin to Bob. Alex alone has the secret keys to authorize that amount. Alex's blockchain public key allows anyone to verify the transaction.
Solution
Now, apply bitcoin to BGP. BGP generals resemble bitcoin nodes. The generals' consensus is like bitcoin nodes' blockchain block selection. Bitcoin software on all nodes can:
Check transactions (i.e., validate digital signatures)
2. Accept and propagate just the first miner to receive the valid hash and verify it accomplished the task. The only way to guess the proper hash is to brute force it by repeatedly producing one with the fixed/current block header and a fresh nonce value.
Thus, PoW and a dispersed network of nodes that accept blocks from miners that solve the unfalsifiable cryptographic challenge solve consensus.
Suppose:
Unreliable nodes
Unreliable miners
Bitcoin accepts the longest chain if rogue nodes cause divergence in accepted blocks. Thus, rogue nodes must outnumber honest nodes in accepting/forming the longer chain for invalid transactions to reach the blockchain. As of November 2022, 7000 coordinated rogue nodes are needed to takeover the bitcoin network.
Dishonest miners could also try to insert blocks with falsified transactions (double spend, reverse, censor, etc.) into the chain. This requires over 50% (51% attack) of miners (total computational power) to outguess the hash and attack the network. Mining hash rate exceeds 200 million (source). Rewards and transaction fees encourage miners to cooperate rather than attack. Quantum computers may become a threat.
Visit my Quantum Computing post.
Quantum computers—what are they? Quantum computers will have a big influence. towardsdatascience.com
Nodes have more power than miners since they can validate transactions and reject fake blocks. Thus, the network is secure if honest nodes are the majority.
Summary
Table 1 compares three Byzantine Generals Problem implementations.
Bitcoin white paper and implementation solved the consensus challenge of distributed systems without central governance. It solved the illusive Byzantine Generals Problem.
Resources
Resources
Source-code for Bitcoin Core Software — https://github.com/bitcoin/bitcoin
Bitcoin white paper — https://bitcoin.org/bitcoin.pdf
https://www.microsoft.com/en-us/research/publication/byzantine-generals-problem/
https://www.microsoft.com/en-us/research/uploads/prod/2016/12/The-Byzantine-Generals-Problem.pdf
Genuinely Distributed Byzantine Machine Learning, El-Mahdi El-Mhamdi et al., 2020. ACM, New York, NY, https://doi.org/10.1145/3382734.3405695
You might also like
Leon Ho
3 years ago
Digital Brainbuilding (Your Second Brain)
The human brain is amazing. As more scientists examine the brain, we learn how much it can store.
The human brain has 1 billion neurons, according to Scientific American. Each neuron creates 1,000 connections, totaling over a trillion. If each neuron could store one memory, we'd run out of room. [1]
What if you could store and access more info, freeing up brain space for problem-solving and creativity?
Build a second brain to keep up with rising knowledge (what I refer to as a Digital Brain). Effectively managing information entails realizing you can't recall everything.
Every action requires information. You need the correct information to learn a new skill, complete a project at work, or establish a business. You must manage information properly to advance your profession and improve your life.
How to construct a second brain to organize information and achieve goals.
What Is a Second Brain?
How often do you forget an article or book's key point? Have you ever wasted hours looking for a saved file?
If so, you're not alone. Information overload affects millions of individuals worldwide. Information overload drains mental resources and causes anxiety.
This is when the second brain comes in.
Building a second brain doesn't involve duplicating the human brain. Building a system that captures, organizes, retrieves, and archives ideas and thoughts. The second brain improves memory, organization, and recall.
Digital tools are preferable to analog for building a second brain.
Digital tools are portable and accessible. Due to these benefits, we'll focus on digital second-brain building.
Brainware
Digital Brains are external hard drives. It stores, organizes, and retrieves. This means improving your memory won't be difficult.
Memory has three components in computing:
Recording — storing the information
Organization — archiving it in a logical manner
Recall — retrieving it again when you need it
For example:
Due to rigorous security settings, many websites need you to create complicated passwords with special characters.
You must now memorize (Record), organize (Organize), and input this new password the next time you check in (Recall).
Even in this simple example, there are many pieces to remember. We can't recognize this new password with our usual patterns. If we don't use the password every day, we'll forget it. You'll type the wrong password when you try to remember it.
It's common. Is it because the information is complicated? Nope. Passwords are basically letters, numbers, and symbols.
It happens because our brains aren't meant to memorize these. Digital Brains can do heavy lifting.
Why You Need a Digital Brain
Dual minds are best. Birth brain is limited.
The cerebral cortex has 125 trillion synapses, according to a Stanford Study. The human brain can hold 2.5 million terabytes of digital data. [2]
Building a second brain improves learning and memory.
Learn and store information effectively
Faster information recall
Organize information to see connections and patterns
Build a Digital Brain to learn more and reach your goals faster. Building a second brain requires time and work, but you'll have more time for vital undertakings.
Why you need a Digital Brain:
1. Use Brainpower Effectively
Your brain has boundaries, like any organ. This is true while solving a complex question or activity. If you can't focus on a work project, you won't finish it on time.
Second brain reduces distractions. A robust structure helps you handle complicated challenges quickly and stay on track. Without distractions, it's easy to focus on vital activities.
2. Staying Organized
Professional and personal duties must be balanced. With so much to do, it's easy to neglect crucial duties. This is especially true for skill-building. Digital Brain will keep you organized and stress-free.
Life success requires action. Organized people get things done. Organizing your information will give you time for crucial tasks.
You'll finish projects faster with good materials and methods. As you succeed, you'll gain creative confidence. You can then tackle greater jobs.
3. Creativity Process
Creativity drives today's world. Creativity is mysterious and surprising for millions worldwide. Immersing yourself in others' associations, triggers, thoughts, and ideas can generate inspiration and creativity.
Building a second brain is crucial to establishing your creative process and building habits that will help you reach your goals. Creativity doesn't require perfection or overthinking.
4. Transforming Your Knowledge Into Opportunities
This is the age of entrepreneurship. Today, you can publish online, build an audience, and make money.
Whether it's a business or hobby, you'll have several job alternatives. Knowledge can boost your economy with ideas and insights.
5. Improving Thinking and Uncovering Connections
Modern career success depends on how you think. Instead of overthinking or perfecting, collect the best images, stories, metaphors, anecdotes, and observations.
This will increase your creativity and reveal connections. Increasing your imagination can help you achieve your goals, according to research. [3]
Your ability to recognize trends will help you stay ahead of the pack.
6. Credibility for a New Job or Business
Your main asset is experience-based expertise. Others won't be able to learn without your help. Technology makes knowledge tangible.
This lets you use your time as you choose while helping others. Changing professions or establishing a new business become learning opportunities when you have a Digital Brain.
7. Using Learning Resources
Millions of people use internet learning materials to improve their lives. Online resources abound. These include books, forums, podcasts, articles, and webinars.
These resources are mostly free or inexpensive. Organizing your knowledge can save you time and money. Building a Digital Brain helps you learn faster. You'll make rapid progress by enjoying learning.
How does a second brain feel?
Digital Brain has helped me arrange my job and family life for years.
No need to remember 1001 passwords. I never forget anything on my wife's grocery lists. Never miss a meeting. I can access essential information and papers anytime, anywhere.
Delegating memory to a second brain reduces tension and anxiety because you'll know what to do with every piece of information.
No information will be forgotten, boosting your confidence. Better manage your fears and concerns by writing them down and establishing a strategy. You'll understand the plethora of daily information and have a clear head.
How to Develop Your Digital Brain (Your Second Brain)
It's cheap but requires work.
Digital Brain development requires:
Recording — storing the information
Organization — archiving it in a logical manner
Recall — retrieving it again when you need it
1. Decide what information matters before recording.
To succeed in today's environment, you must manage massive amounts of data. Articles, books, webinars, podcasts, emails, and texts provide value. Remembering everything is impossible and overwhelming.
What information do you need to achieve your goals?
You must consolidate ideas and create a strategy to reach your aims. Your biological brain can imagine and create with a Digital Brain.
2. Use the Right Tool
We usually record information without any preparation - we brainstorm in a word processor, email ourselves a message, or take notes while reading.
This information isn't used. You must store information in a central location.
Different information needs different instruments.
Evernote is a top note-taking program. Audio clips, Slack chats, PDFs, text notes, photos, scanned handwritten pages, emails, and webpages can be added.
Pocket is a great software for saving and organizing content. Images, videos, and text can be sorted. Web-optimized design
Calendar apps help you manage your time and enhance your productivity by reminding you of your most important tasks. Calendar apps flourish. The best calendar apps are easy to use, have many features, and work across devices. These calendars include Google, Apple, and Outlook.
To-do list/checklist apps are useful for managing tasks. Easy-to-use, versatility, budget, and cross-platform compatibility are important when picking to-do list apps. Google Keep, Google Tasks, and Apple Notes are good to-do apps.
3. Organize data for easy retrieval
How should you organize collected data?
When you collect and organize data, you'll see connections. An article about networking can assist you comprehend web marketing. Saved business cards can help you find new clients.
Choosing the correct tools helps organize data. Here are some tools selection criteria:
Can the tool sync across devices?
Personal or team?
Has a search function for easy information retrieval?
Does it provide easy data categorization?
Can users create lists or collections?
Does it offer easy idea-information connections?
Does it mind map and visually organize thoughts?
Conclusion
Building a Digital Brain (second brain) helps us save information, think creatively, and implement ideas. Your second brain is a biological extension. It prevents amnesia, allowing you to tackle bigger creative difficulties.
People who love learning often consume information without using it. Every day, they postpone life-improving experiences until they're forgotten. Useful information becomes strength.
Reference
[1] ^ Scientific American: What Is the Memory Capacity of the Human Brain?
[2] ^ Clinical Neurology Specialists: What is the Memory Capacity of a Human Brain?
[3] ^ National Library of Medicine: Imagining Success: Multiple Achievement Goals and the Effectiveness of Imagery
Quant Galore
3 years ago
I created BAW-IV Trading because I was short on money.
More retail traders means faster, more sophisticated, and more successful methods.
Tech specifications
Only requires a laptop and an internet connection.
We'll use OpenBB's research platform for data/analysis.
Pricing and execution on Options-Quant
Background
You don't need to know the arithmetic details to use this method.
Black-Scholes is a popular option pricing model. It's best for pricing European options. European options are only exercisable at expiration, unlike American options. American options are always exercisable.
American options carry a premium to cover for the risk of early exercise. The Black-Scholes model doesn't account for this premium, hence it can't price genuine, traded American options.
Barone-Adesi-Whaley (BAW) model. BAW modifies Black-Scholes. It accounts for exercise risk premium and stock dividends. It adds the option's early exercise value to the Black-Scholes value.
The trader need not know the formulaic derivations of this model.
https://ir.nctu.edu.tw/bitstream/11536/14182/1/000264318900005.pdf
Strategy
This strategy targets implied volatility. First, we'll locate liquid options that expire within 30 days and have minimal implied volatility.
After selecting the option that meets the requirements, we price it to get the BAW implied volatility (we choose BAW because it's a more accurate Black-Scholes model). If estimated implied volatility is larger than market volatility, we'll capture the spread.
(Calculated IV — Market IV) = (Profit)
Some approaches to target implied volatility are pricey and inaccessible to individual investors. The best and most cost-effective alternative is to acquire a straddle and delta hedge. This may sound terrifying and pricey, but as shown below, it's much less so.
The Trade
First, we want to find our ideal option, so we use OpenBB terminal to screen for options that:
Have an IV at least 5% lower than the 20-day historical IV
Are no more than 5% out-of-the-money
Expire in less than 30 days
We query:
stocks/options/screen/set low_IV/scr --export Output.csv
This uses the screener function to screen for options that satisfy the above criteria, which we specify in the low IV preset (more on custom presets here). It then saves the matching results to a csv(Excel) file for viewing and analysis.
Stick to liquid names like SPY, AAPL, and QQQ since getting out of a position is just as crucial as getting in. Smaller, illiquid names have higher inefficiencies, which could restrict total profits.
We calculate IV using the BAWbisection model (the bisection is a method of calculating IV, more can be found here.) We price the IV first.
According to the BAW model, implied volatility at this level should be priced at 26.90%. When re-pricing the put, IV is 24.34%, up 3%.
Now it's evident. We must purchase the straddle (long the call and long the put) assuming the computed implied volatility is more appropriate and efficient than the market's. We just want to speculate on volatility, not price fluctuations, thus we delta hedge.
The Fun Starts
We buy both options for $7.65. (x100 multiplier). Initial delta is 2. For every dollar the stock price swings up or down, our position value moves $2.
We want delta to be 0 to avoid price vulnerability. A delta of 0 suggests our position's value won't change from underlying price changes. Being delta-hedged allows us to profit/lose from implied volatility. Shorting 2 shares makes us delta-neutral.
That's delta hedging. (Share price * shares traded) = $330.7 to become delta-neutral. You may have noted that delta is not truly 0.00. This is common since delta-hedging means getting as near to 0 as feasible, since it is rare for deltas to align at 0.00.
Now we're vulnerable to changes in Vega (and Gamma, but given we're dynamically hedging, it's not a big risk), or implied volatility. We wanted to gamble that the position's IV would climb by at least 2%, so we'll maintain it delta-hedged and watch IV.
Because the underlying moves continually, the option's delta moves continuously. A trader can short/long 5 AAPL shares at most. Paper trading lets you practice delta-hedging. Being quick-footed will help with this tactic.
Profit-Closing
As expected, implied volatility rose. By 10 minutes before market closure, the call's implied vol rose to 27% and the put's to 24%. This allowed us to sell the call for $4.95 and the put for $4.35, creating a profit of $165.
You may pull historical data to see how this trade performed. Note the implied volatility and pricing in the final options chain for August 5, 2022 (the position date).
Final Thoughts
Congratulations, that was a doozy. To reiterate, we identified tickers prone to increased implied volatility by screening OpenBB's low IV setting. We double-checked the IV by plugging the price into Options-BAW Quant's model. When volatility was off, we bought a straddle and delta-hedged it. Finally, implied volatility returned to a normal level, and we profited on the spread.
The retail trading space is very quickly catching up to that of institutions. Commissions and fees used to kill this method, but now they cost less than $5. Watching momentum, technical analysis, and now quantitative strategies evolve is intriguing.
I'm not linked with these sites and receive no financial benefit from my writing.
Tell me how your experience goes and how I helped; I love success tales.
Daniel Clery
3 years ago
Twisted device investigates fusion alternatives
German stellarator revamped to run longer, hotter, compete with tokamaks
Tokamaks have dominated the search for fusion energy for decades. Just as ITER, the world's largest and most expensive tokamak, nears completion in southern France, a smaller, twistier testbed will start up in Germany.
If the 16-meter-wide stellarator can match or outperform similar-size tokamaks, fusion experts may rethink their future. Stellarators can keep their superhot gases stable enough to fuse nuclei and produce energy. They can theoretically run forever, but tokamaks must pause to reset their magnet coils.
The €1 billion German machine, Wendelstein 7-X (W7-X), is already getting "tokamak-like performance" in short runs, claims plasma physicist David Gates, preventing particles and heat from escaping the superhot gas. If W7-X can go long, "it will be ahead," he says. "Stellarators excel" Eindhoven University of Technology theorist Josefine Proll says, "Stellarators are back in the game." A few of startup companies, including one that Gates is leaving Princeton Plasma Physics Laboratory, are developing their own stellarators.
W7-X has been running at the Max Planck Institute for Plasma Physics (IPP) in Greifswald, Germany, since 2015, albeit only at low power and for brief runs. W7-X's developers took it down and replaced all inner walls and fittings with water-cooled equivalents, allowing for longer, hotter runs. The team reported at a W7-X board meeting last week that the revised plasma vessel has no leaks. It's expected to restart later this month to show if it can get plasma to fusion-igniting conditions.
Wendelstein 7-X's water-cooled inner surface allows for longer runs.
HOSAN/IPP
Both stellarators and tokamaks create magnetic gas cages hot enough to melt metal. Microwaves or particle beams heat. Extreme temperatures create a plasma, a seething mix of separated nuclei and electrons, and cause the nuclei to fuse, releasing energy. A fusion power plant would use deuterium and tritium, which react quickly. Non-energy-generating research machines like W7-X avoid tritium and use hydrogen or deuterium instead.
Tokamaks and stellarators use electromagnetic coils to create plasma-confining magnetic fields. A greater field near the hole causes plasma to drift to the reactor's wall.
Tokamaks control drift by circulating plasma around a ring. Streaming creates a magnetic field that twists and stabilizes ionized plasma. Stellarators employ magnetic coils to twist, not plasma. Once plasma physicists got powerful enough supercomputers, they could optimize stellarator magnets to improve plasma confinement.
W7-X is the first large, optimized stellarator with 50 6- ton superconducting coils. Its construction began in the mid-1990s and cost roughly twice the €550 million originally budgeted.
The wait hasn't disappointed researchers. W7-X director Thomas Klinger: "The machine operated immediately." "It's a friendly machine." It did everything we asked." Tokamaks are prone to "instabilities" (plasma bulging or wobbling) or strong "disruptions," sometimes associated to halted plasma flow. IPP theorist Sophia Henneberg believes stellarators don't employ plasma current, which "removes an entire branch" of instabilities.
In early stellarators, the magnetic field geometry drove slower particles to follow banana-shaped orbits until they collided with other particles and leaked energy. Gates believes W7-X's ability to suppress this effect implies its optimization works.
W7-X loses heat through different forms of turbulence, which push particles toward the wall. Theorists have only lately mastered simulating turbulence. W7-X's forthcoming campaign will test simulations and turbulence-fighting techniques.
A stellarator can run constantly, unlike a tokamak, which pulses. W7-X has run 100 seconds—long by tokamak standards—at low power. The device's uncooled microwave and particle heating systems only produced 11.5 megawatts. The update doubles heating power. High temperature, high plasma density, and extensive runs will test stellarators' fusion power potential. Klinger wants to heat ions to 50 million degrees Celsius for 100 seconds. That would make W7-X "a world-class machine," he argues. The team will push for 30 minutes. "We'll move step-by-step," he says.
W7-X's success has inspired VCs to finance entrepreneurs creating commercial stellarators. Startups must simplify magnet production.
Princeton Stellarators, created by Gates and colleagues this year, has $3 million to build a prototype reactor without W7-X's twisted magnet coils. Instead, it will use a mosaic of 1000 HTS square coils on the plasma vessel's outside. By adjusting each coil's magnetic field, operators can change the applied field's form. Gates: "It moves coil complexity to the control system." The company intends to construct a reactor that can fuse cheap, abundant deuterium to produce neutrons for radioisotopes. If successful, the company will build a reactor.
Renaissance Fusion, situated in Grenoble, France, raised €16 million and wants to coat plasma vessel segments in HTS. Using a laser, engineers will burn off superconductor tracks to carve magnet coils. They want to build a meter-long test segment in 2 years and a full prototype by 2027.
Type One Energy in Madison, Wisconsin, won DOE money to bend HTS cables for stellarator magnets. The business carved twisting grooves in metal with computer-controlled etching equipment to coil cables. David Anderson of the University of Wisconsin, Madison, claims advanced manufacturing technology enables the stellarator.
Anderson said W7-X's next phase will boost stellarator work. “Half-hour discharges are steady-state,” he says. “This is a big deal.”